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Probability Question with 2 rolls
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I have a probability question.
Say that there is a 2% chance of something occuring and then a 1d5 (20%) of it being a critical success.
So technically its a 0.4% chance of a critical success.
If we have more rolls, say 100 rolls. Would it still be a 0.4% for a critical success or would you have a higher chance?
probability dice
asked Jul 31 at 18:35
Apple
6
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up vote
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I have a probability question.
Say that there is a 2% chance of something occuring and then a 1d5 (20%) of it being a critical success.
So technically its a 0.4% chance of a critical success.
If we have more rolls, say 100 rolls. Would it still be a 0.4% for a critical success or would you have a higher chance?
probability dice
asked Jul 31 at 18:35
Apple
6
1
If you want to calculate the probability of at least one success, then subtract the probability that none of the rolls result in a success from $1$. You will find that the probability is greater than $0.4%$ since there are more opportunities for a success to occur.
– N. F. Taussig
Jul 31 at 18:43
If $X sim mathsfBinom(n=100, p=.004),$ then $P(X ge 1) = 1 - P(X=0).$ In R statistical software the statement1 - dbinom(0, 100, .004)returns 0..3302174
– BruceET
Aug 1 at 1:43
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have a probability question.
Say that there is a 2% chance of something occuring and then a 1d5 (20%) of it being a critical success.
So technically its a 0.4% chance of a critical success.
If we have more rolls, say 100 rolls. Would it still be a 0.4% for a critical success or would you have a higher chance?
probability dice
asked Jul 31 at 18:35
Apple
6
I have a probability question.
Say that there is a 2% chance of something occuring and then a 1d5 (20%) of it being a critical success.
So technically its a 0.4% chance of a critical success.
If we have more rolls, say 100 rolls. Would it still be a 0.4% for a critical success or would you have a higher chance?
probability dice
asked Jul 31 at 18:35
Apple
6
asked Jul 31 at 18:35
Apple
6
asked Jul 31 at 18:35
Apple
6
asked Jul 31 at 18:35
Apple
6
6
1
If you want to calculate the probability of at least one success, then subtract the probability that none of the rolls result in a success from $1$. You will find that the probability is greater than $0.4%$ since there are more opportunities for a success to occur.
– N. F. Taussig
Jul 31 at 18:43
If $X sim mathsfBinom(n=100, p=.004),$ then $P(X ge 1) = 1 - P(X=0).$ In R statistical software the statement1 - dbinom(0, 100, .004)returns 0..3302174
– BruceET
Aug 1 at 1:43
add a comment |Â
1
If you want to calculate the probability of at least one success, then subtract the probability that none of the rolls result in a success from $1$. You will find that the probability is greater than $0.4%$ since there are more opportunities for a success to occur.
– N. F. Taussig
Jul 31 at 18:43
If $X sim mathsfBinom(n=100, p=.004),$ then $P(X ge 1) = 1 - P(X=0).$ In R statistical software the statement1 - dbinom(0, 100, .004)returns 0..3302174
– BruceET
Aug 1 at 1:43
1
1
If you want to calculate the probability of at least one success, then subtract the probability that none of the rolls result in a success from $1$. You will find that the probability is greater than $0.4%$ since there are more opportunities for a success to occur.
– N. F. Taussig
Jul 31 at 18:43
If you want to calculate the probability of at least one success, then subtract the probability that none of the rolls result in a success from $1$. You will find that the probability is greater than $0.4%$ since there are more opportunities for a success to occur.
– N. F. Taussig
Jul 31 at 18:43
If $X sim mathsfBinom(n=100, p=.004),$ then $P(X ge 1) = 1 - P(X=0).$ In R statistical software the statement
1 - dbinom(0, 100, .004) returns 0..3302174– BruceET
Aug 1 at 1:43
If $X sim mathsfBinom(n=100, p=.004),$ then $P(X ge 1) = 1 - P(X=0).$ In R statistical software the statement
1 - dbinom(0, 100, .004) returns 0..3302174– BruceET
Aug 1 at 1:43
add a comment |Â
1 Answer
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For independent rolls, the chance of no critical success is the chance of not getting critical success on one roll, times $100$:
$P_0 = (1 - 0.004)^100=0.996^100 doteq 0.6698.$
Then, the probability of getting critical success on at least one roll of a hundred is
$P_>0 = 1 - 0.996^100 doteq 0.3302,$
or about $1/3$.
answered Jul 31 at 19:23
John
21.9k32346
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
For independent rolls, the chance of no critical success is the chance of not getting critical success on one roll, times $100$:
$P_0 = (1 - 0.004)^100=0.996^100 doteq 0.6698.$
Then, the probability of getting critical success on at least one roll of a hundred is
$P_>0 = 1 - 0.996^100 doteq 0.3302,$
or about $1/3$.
answered Jul 31 at 19:23
John
21.9k32346
add a comment |Â
up vote
0
down vote
For independent rolls, the chance of no critical success is the chance of not getting critical success on one roll, times $100$:
$P_0 = (1 - 0.004)^100=0.996^100 doteq 0.6698.$
Then, the probability of getting critical success on at least one roll of a hundred is
$P_>0 = 1 - 0.996^100 doteq 0.3302,$
or about $1/3$.
answered Jul 31 at 19:23
John
21.9k32346
add a comment |Â
up vote
0
down vote
up vote
0
down vote
For independent rolls, the chance of no critical success is the chance of not getting critical success on one roll, times $100$:
$P_0 = (1 - 0.004)^100=0.996^100 doteq 0.6698.$
Then, the probability of getting critical success on at least one roll of a hundred is
$P_>0 = 1 - 0.996^100 doteq 0.3302,$
or about $1/3$.
answered Jul 31 at 19:23
John
21.9k32346
For independent rolls, the chance of no critical success is the chance of not getting critical success on one roll, times $100$:
$P_0 = (1 - 0.004)^100=0.996^100 doteq 0.6698.$
Then, the probability of getting critical success on at least one roll of a hundred is
$P_>0 = 1 - 0.996^100 doteq 0.3302,$
or about $1/3$.
answered Jul 31 at 19:23
John
21.9k32346
answered Jul 31 at 19:23
John
21.9k32346
answered Jul 31 at 19:23
John
21.9k32346
answered Jul 31 at 19:23
John
21.9k32346
21.9k32346
add a comment |Â
add a comment |Â
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1
If you want to calculate the probability of at least one success, then subtract the probability that none of the rolls result in a success from $1$. You will find that the probability is greater than $0.4%$ since there are more opportunities for a success to occur.
– N. F. Taussig
Jul 31 at 18:43
If $X sim mathsfBinom(n=100, p=.004),$ then $P(X ge 1) = 1 - P(X=0).$ In R statistical software the statement
1 - dbinom(0, 100, .004)returns 0..3302174– BruceET
Aug 1 at 1:43