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Suppose a die is thrown .Write two events which are ..
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Suppose a die is tossed. Write two events which are:
a. Exhaustive and mutually exclusive.
b. Exhaustive but not mutually exclusive.
c. Exhaustive but not equally likely
My input :
a. Events are :
$A=$ Getting even number when die is thrown.
$B=$ Getting odd number when die is thrown.
b. Events are :
$A=$ Getting number less than $5$ when die is thrown.
$B=$ Getting multiple of $2$ when die is thrown.
Did I write them correctly?
c. I am stuck at this one. Honestly, I didn't understand the "not equally likely or equally likely". Please, someone, tell me the meaning of it and one example of it too. Don't give an example related to this particular question, after getting understanding of it I 'll try to make one by myself.
probability
asked Aug 2 at 13:18
Damn1o1
56613
 |Â
show 6 more comments
up vote
0
down vote
favorite
Suppose a die is tossed. Write two events which are:
a. Exhaustive and mutually exclusive.
b. Exhaustive but not mutually exclusive.
c. Exhaustive but not equally likely
My input :
a. Events are :
$A=$ Getting even number when die is thrown.
$B=$ Getting odd number when die is thrown.
b. Events are :
$A=$ Getting number less than $5$ when die is thrown.
$B=$ Getting multiple of $2$ when die is thrown.
Did I write them correctly?
c. I am stuck at this one. Honestly, I didn't understand the "not equally likely or equally likely". Please, someone, tell me the meaning of it and one example of it too. Don't give an example related to this particular question, after getting understanding of it I 'll try to make one by myself.
probability
asked Aug 2 at 13:18
Damn1o1
56613
1
An unrelated example of "exhaustive but not equally likely" would be...suppose you flip a fair coin twice. let $A$ be the event "you get $TT$". Let $B$ be the event "you get at least one $H$".
– lulu
Aug 2 at 13:25
1
Note: I revised my comment to make my example unrelated to your question. Also, I realized I had misread your question. Your first example is good, but your second is not as the event $5$ does not appear.
– lulu
Aug 2 at 13:25
1
In c) you are asked to mention two events such that it is for certain that at least one of the events will occur, and secondly they must have distinct probability to occur.
– drhab
Aug 2 at 13:34
1
@drhab It means Event A: Getting number less than or equal to 4 has a probability frac46. and another event B: Getting number 5 or 6 has a probability frac26. Both events have a different probability which means they are not equally likely to occur. I get it right?
– Damn1o1
Aug 2 at 13:40
1
That is a correct example. Btw, it is not forbidden (and also not needed) here that both events can occur (as is the case in a)).
– drhab
Aug 2 at 13:43
 |Â
show 6 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Suppose a die is tossed. Write two events which are:
a. Exhaustive and mutually exclusive.
b. Exhaustive but not mutually exclusive.
c. Exhaustive but not equally likely
My input :
a. Events are :
$A=$ Getting even number when die is thrown.
$B=$ Getting odd number when die is thrown.
b. Events are :
$A=$ Getting number less than $5$ when die is thrown.
$B=$ Getting multiple of $2$ when die is thrown.
Did I write them correctly?
c. I am stuck at this one. Honestly, I didn't understand the "not equally likely or equally likely". Please, someone, tell me the meaning of it and one example of it too. Don't give an example related to this particular question, after getting understanding of it I 'll try to make one by myself.
probability
asked Aug 2 at 13:18
Damn1o1
56613
Suppose a die is tossed. Write two events which are:
a. Exhaustive and mutually exclusive.
b. Exhaustive but not mutually exclusive.
c. Exhaustive but not equally likely
My input :
a. Events are :
$A=$ Getting even number when die is thrown.
$B=$ Getting odd number when die is thrown.
b. Events are :
$A=$ Getting number less than $5$ when die is thrown.
$B=$ Getting multiple of $2$ when die is thrown.
Did I write them correctly?
c. I am stuck at this one. Honestly, I didn't understand the "not equally likely or equally likely". Please, someone, tell me the meaning of it and one example of it too. Don't give an example related to this particular question, after getting understanding of it I 'll try to make one by myself.
probability
asked Aug 2 at 13:18
Damn1o1
56613
edited Aug 2 at 13:23
user223391
asked Aug 2 at 13:18
Damn1o1
56613
asked Aug 2 at 13:18
Damn1o1
56613
asked Aug 2 at 13:18
Damn1o1
56613
56613
1
An unrelated example of "exhaustive but not equally likely" would be...suppose you flip a fair coin twice. let $A$ be the event "you get $TT$". Let $B$ be the event "you get at least one $H$".
– lulu
Aug 2 at 13:25
1
Note: I revised my comment to make my example unrelated to your question. Also, I realized I had misread your question. Your first example is good, but your second is not as the event $5$ does not appear.
– lulu
Aug 2 at 13:25
1
In c) you are asked to mention two events such that it is for certain that at least one of the events will occur, and secondly they must have distinct probability to occur.
– drhab
Aug 2 at 13:34
1
@drhab It means Event A: Getting number less than or equal to 4 has a probability frac46. and another event B: Getting number 5 or 6 has a probability frac26. Both events have a different probability which means they are not equally likely to occur. I get it right?
– Damn1o1
Aug 2 at 13:40
1
That is a correct example. Btw, it is not forbidden (and also not needed) here that both events can occur (as is the case in a)).
– drhab
Aug 2 at 13:43
 |Â
show 6 more comments
1
An unrelated example of "exhaustive but not equally likely" would be...suppose you flip a fair coin twice. let $A$ be the event "you get $TT$". Let $B$ be the event "you get at least one $H$".
– lulu
Aug 2 at 13:25
1
Note: I revised my comment to make my example unrelated to your question. Also, I realized I had misread your question. Your first example is good, but your second is not as the event $5$ does not appear.
– lulu
Aug 2 at 13:25
1
In c) you are asked to mention two events such that it is for certain that at least one of the events will occur, and secondly they must have distinct probability to occur.
– drhab
Aug 2 at 13:34
1
@drhab It means Event A: Getting number less than or equal to 4 has a probability frac46. and another event B: Getting number 5 or 6 has a probability frac26. Both events have a different probability which means they are not equally likely to occur. I get it right?
– Damn1o1
Aug 2 at 13:40
1
That is a correct example. Btw, it is not forbidden (and also not needed) here that both events can occur (as is the case in a)).
– drhab
Aug 2 at 13:43
1
1
An unrelated example of "exhaustive but not equally likely" would be...suppose you flip a fair coin twice. let $A$ be the event "you get $TT$". Let $B$ be the event "you get at least one $H$".
– lulu
Aug 2 at 13:25
An unrelated example of "exhaustive but not equally likely" would be...suppose you flip a fair coin twice. let $A$ be the event "you get $TT$". Let $B$ be the event "you get at least one $H$".
– lulu
Aug 2 at 13:25
1
1
Note: I revised my comment to make my example unrelated to your question. Also, I realized I had misread your question. Your first example is good, but your second is not as the event $5$ does not appear.
– lulu
Aug 2 at 13:25
Note: I revised my comment to make my example unrelated to your question. Also, I realized I had misread your question. Your first example is good, but your second is not as the event $5$ does not appear.
– lulu
Aug 2 at 13:25
1
1
In c) you are asked to mention two events such that it is for certain that at least one of the events will occur, and secondly they must have distinct probability to occur.
– drhab
Aug 2 at 13:34
In c) you are asked to mention two events such that it is for certain that at least one of the events will occur, and secondly they must have distinct probability to occur.
– drhab
Aug 2 at 13:34
1
1
@drhab It means Event A: Getting number less than or equal to 4 has a probability frac46. and another event B: Getting number 5 or 6 has a probability frac26. Both events have a different probability which means they are not equally likely to occur. I get it right?
– Damn1o1
Aug 2 at 13:40
@drhab It means Event A: Getting number less than or equal to 4 has a probability frac46. and another event B: Getting number 5 or 6 has a probability frac26. Both events have a different probability which means they are not equally likely to occur. I get it right?
– Damn1o1
Aug 2 at 13:40
1
1
That is a correct example. Btw, it is not forbidden (and also not needed) here that both events can occur (as is the case in a)).
– drhab
Aug 2 at 13:43
That is a correct example. Btw, it is not forbidden (and also not needed) here that both events can occur (as is the case in a)).
– drhab
Aug 2 at 13:43
 |Â
show 6 more comments
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Let S be the universal set
Set S :1,2,3,4,5,6
Set A :your choice $A in S$
Set B :your choice $B in S$
Exhaustive Events: You can choose any way you want to define A and B such that $Acup B$ = S
Example :
|A =1 B=2,3,4,5,6|
|A =1,3 B=2,4,5,6|
|A =1,2,5,6 B=3,4|
|A =1,2,3,6 B=2,3,4,5|
|A =1,2,3 B=2,3,4,5,6|
|A =1,2,3,4,5 B=1,2,3,4,5,6| .....
Mutually Exclusive : You can choose any way you want to define A and B such that $A cap B$ = $phi $
i.e. There should be no common element between A and B
Example :
|A =1 B=2,3,4,5,6|
|A =1,3 B=2,4,5,6|
|A =1,2,5,6 B=3,4|
|A =1,2,3 B=4,5|
|A =1 B=2,3|
|A =1,6 B=2,4,5| .....
Equally likely: It means the probability of occurring of events A and B is same
Here probability is determined by the size of set A and B.
For equally likely both sets have the same size
Examples for equally likely
|A =1,2,3 B=2,3,4|
|A =1,3 B=4,5|
|A =1,2 B=1,2|
|A =1,3,5 B=2,4,6|
|A =1 B=6|
|A =1,4,5,6 B=2,3,4,5| .....
answered Aug 2 at 15:51
NewGuy
30617
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Let S be the universal set
Set S :1,2,3,4,5,6
Set A :your choice $A in S$
Set B :your choice $B in S$
Exhaustive Events: You can choose any way you want to define A and B such that $Acup B$ = S
Example :
|A =1 B=2,3,4,5,6|
|A =1,3 B=2,4,5,6|
|A =1,2,5,6 B=3,4|
|A =1,2,3,6 B=2,3,4,5|
|A =1,2,3 B=2,3,4,5,6|
|A =1,2,3,4,5 B=1,2,3,4,5,6| .....
Mutually Exclusive : You can choose any way you want to define A and B such that $A cap B$ = $phi $
i.e. There should be no common element between A and B
Example :
|A =1 B=2,3,4,5,6|
|A =1,3 B=2,4,5,6|
|A =1,2,5,6 B=3,4|
|A =1,2,3 B=4,5|
|A =1 B=2,3|
|A =1,6 B=2,4,5| .....
Equally likely: It means the probability of occurring of events A and B is same
Here probability is determined by the size of set A and B.
For equally likely both sets have the same size
Examples for equally likely
|A =1,2,3 B=2,3,4|
|A =1,3 B=4,5|
|A =1,2 B=1,2|
|A =1,3,5 B=2,4,6|
|A =1 B=6|
|A =1,4,5,6 B=2,3,4,5| .....
answered Aug 2 at 15:51
NewGuy
30617
add a comment |Â
up vote
1
down vote
accepted
Let S be the universal set
Set S :1,2,3,4,5,6
Set A :your choice $A in S$
Set B :your choice $B in S$
Exhaustive Events: You can choose any way you want to define A and B such that $Acup B$ = S
Example :
|A =1 B=2,3,4,5,6|
|A =1,3 B=2,4,5,6|
|A =1,2,5,6 B=3,4|
|A =1,2,3,6 B=2,3,4,5|
|A =1,2,3 B=2,3,4,5,6|
|A =1,2,3,4,5 B=1,2,3,4,5,6| .....
Mutually Exclusive : You can choose any way you want to define A and B such that $A cap B$ = $phi $
i.e. There should be no common element between A and B
Example :
|A =1 B=2,3,4,5,6|
|A =1,3 B=2,4,5,6|
|A =1,2,5,6 B=3,4|
|A =1,2,3 B=4,5|
|A =1 B=2,3|
|A =1,6 B=2,4,5| .....
Equally likely: It means the probability of occurring of events A and B is same
Here probability is determined by the size of set A and B.
For equally likely both sets have the same size
Examples for equally likely
|A =1,2,3 B=2,3,4|
|A =1,3 B=4,5|
|A =1,2 B=1,2|
|A =1,3,5 B=2,4,6|
|A =1 B=6|
|A =1,4,5,6 B=2,3,4,5| .....
answered Aug 2 at 15:51
NewGuy
30617
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Let S be the universal set
Set S :1,2,3,4,5,6
Set A :your choice $A in S$
Set B :your choice $B in S$
Exhaustive Events: You can choose any way you want to define A and B such that $Acup B$ = S
Example :
|A =1 B=2,3,4,5,6|
|A =1,3 B=2,4,5,6|
|A =1,2,5,6 B=3,4|
|A =1,2,3,6 B=2,3,4,5|
|A =1,2,3 B=2,3,4,5,6|
|A =1,2,3,4,5 B=1,2,3,4,5,6| .....
Mutually Exclusive : You can choose any way you want to define A and B such that $A cap B$ = $phi $
i.e. There should be no common element between A and B
Example :
|A =1 B=2,3,4,5,6|
|A =1,3 B=2,4,5,6|
|A =1,2,5,6 B=3,4|
|A =1,2,3 B=4,5|
|A =1 B=2,3|
|A =1,6 B=2,4,5| .....
Equally likely: It means the probability of occurring of events A and B is same
Here probability is determined by the size of set A and B.
For equally likely both sets have the same size
Examples for equally likely
|A =1,2,3 B=2,3,4|
|A =1,3 B=4,5|
|A =1,2 B=1,2|
|A =1,3,5 B=2,4,6|
|A =1 B=6|
|A =1,4,5,6 B=2,3,4,5| .....
answered Aug 2 at 15:51
NewGuy
30617
Let S be the universal set
Set S :1,2,3,4,5,6
Set A :your choice $A in S$
Set B :your choice $B in S$
Exhaustive Events: You can choose any way you want to define A and B such that $Acup B$ = S
Example :
|A =1 B=2,3,4,5,6|
|A =1,3 B=2,4,5,6|
|A =1,2,5,6 B=3,4|
|A =1,2,3,6 B=2,3,4,5|
|A =1,2,3 B=2,3,4,5,6|
|A =1,2,3,4,5 B=1,2,3,4,5,6| .....
Mutually Exclusive : You can choose any way you want to define A and B such that $A cap B$ = $phi $
i.e. There should be no common element between A and B
Example :
|A =1 B=2,3,4,5,6|
|A =1,3 B=2,4,5,6|
|A =1,2,5,6 B=3,4|
|A =1,2,3 B=4,5|
|A =1 B=2,3|
|A =1,6 B=2,4,5| .....
Equally likely: It means the probability of occurring of events A and B is same
Here probability is determined by the size of set A and B.
For equally likely both sets have the same size
Examples for equally likely
|A =1,2,3 B=2,3,4|
|A =1,3 B=4,5|
|A =1,2 B=1,2|
|A =1,3,5 B=2,4,6|
|A =1 B=6|
|A =1,4,5,6 B=2,3,4,5| .....
answered Aug 2 at 15:51
NewGuy
30617
answered Aug 2 at 15:51
NewGuy
30617
answered Aug 2 at 15:51
NewGuy
30617
answered Aug 2 at 15:51
NewGuy
30617
30617
add a comment |Â
add a comment |Â
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1
An unrelated example of "exhaustive but not equally likely" would be...suppose you flip a fair coin twice. let $A$ be the event "you get $TT$". Let $B$ be the event "you get at least one $H$".
– lulu
Aug 2 at 13:25
1
Note: I revised my comment to make my example unrelated to your question. Also, I realized I had misread your question. Your first example is good, but your second is not as the event $5$ does not appear.
– lulu
Aug 2 at 13:25
1
In c) you are asked to mention two events such that it is for certain that at least one of the events will occur, and secondly they must have distinct probability to occur.
– drhab
Aug 2 at 13:34
1
@drhab It means Event A: Getting number less than or equal to 4 has a probability frac46. and another event B: Getting number 5 or 6 has a probability frac26. Both events have a different probability which means they are not equally likely to occur. I get it right?
– Damn1o1
Aug 2 at 13:40
1
That is a correct example. Btw, it is not forbidden (and also not needed) here that both events can occur (as is the case in a)).
– drhab
Aug 2 at 13:43