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Intresting Probability problem [closed]
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Suppose that, over the course of the next year, a particular investment fund has a 40% probability of beating the market and a 60% probability of under-performing (perhaps they are poorly managed, or charge high fees). If the fund outperforms the market it will (certainly) continue operating for another year, but it is in danger if it under-performs: in that case there's a 50% probability that its investors will angrily withdraw their money, so that the fund simply ceases to exist.
If the fund still exists at the end of the year, what's the probability that it beat the market? You'll find that it's higher than the prior probability of 40%.
probability
asked Jul 16 at 17:18
Parag Jain
86
closed as off-topic by openspace, Alex Francisco, Xander Henderson, Leucippus, Parcly Taxel Jul 17 at 1:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – openspace, Alex Francisco, Xander Henderson, Leucippus, Parcly Taxel
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Suppose that, over the course of the next year, a particular investment fund has a 40% probability of beating the market and a 60% probability of under-performing (perhaps they are poorly managed, or charge high fees). If the fund outperforms the market it will (certainly) continue operating for another year, but it is in danger if it under-performs: in that case there's a 50% probability that its investors will angrily withdraw their money, so that the fund simply ceases to exist.
If the fund still exists at the end of the year, what's the probability that it beat the market? You'll find that it's higher than the prior probability of 40%.
probability
asked Jul 16 at 17:18
Parag Jain
86
closed as off-topic by openspace, Alex Francisco, Xander Henderson, Leucippus, Parcly Taxel Jul 17 at 1:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – openspace, Alex Francisco, Xander Henderson, Leucippus, Parcly Taxel
add a comment |Â
up vote
0
down vote
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up vote
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down vote
favorite
Suppose that, over the course of the next year, a particular investment fund has a 40% probability of beating the market and a 60% probability of under-performing (perhaps they are poorly managed, or charge high fees). If the fund outperforms the market it will (certainly) continue operating for another year, but it is in danger if it under-performs: in that case there's a 50% probability that its investors will angrily withdraw their money, so that the fund simply ceases to exist.
If the fund still exists at the end of the year, what's the probability that it beat the market? You'll find that it's higher than the prior probability of 40%.
probability
asked Jul 16 at 17:18
Parag Jain
86
Suppose that, over the course of the next year, a particular investment fund has a 40% probability of beating the market and a 60% probability of under-performing (perhaps they are poorly managed, or charge high fees). If the fund outperforms the market it will (certainly) continue operating for another year, but it is in danger if it under-performs: in that case there's a 50% probability that its investors will angrily withdraw their money, so that the fund simply ceases to exist.
If the fund still exists at the end of the year, what's the probability that it beat the market? You'll find that it's higher than the prior probability of 40%.
probability
asked Jul 16 at 17:18
Parag Jain
86
asked Jul 16 at 17:18
Parag Jain
86
asked Jul 16 at 17:18
Parag Jain
86
asked Jul 16 at 17:18
Parag Jain
86
86
closed as off-topic by openspace, Alex Francisco, Xander Henderson, Leucippus, Parcly Taxel Jul 17 at 1:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – openspace, Alex Francisco, Xander Henderson, Leucippus, Parcly Taxel
closed as off-topic by openspace, Alex Francisco, Xander Henderson, Leucippus, Parcly Taxel Jul 17 at 1:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – openspace, Alex Francisco, Xander Henderson, Leucippus, Parcly Taxel
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1 Answer
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Ah, this is a problem regarding conditional probability. We define a probability space $Omega = a, b, c$, where
- $a$ means that the fund has beat the market,
- $b$ means that the fund has not beat the market, and the investors did not withdraw,
- and $c$ means that the fund has not beat the market, and the investors withdrew their money.
Now from the assumption, it follows that if $P$ is the probability measure, then $P(a) = 0.4$, and $P(X) = 0.6$, where $X = b,c$ is the event that the fund underperformed. Moreover,
$$
P(c|X) = 0.5 = P(b|X).
$$
But since $c cap X = c$ and $b cap X = b$, we may deduce from that that
$$
P(c) = P(b) = 0.5*0.6 = 0.3.
$$
Now note that the event that the fund still exists is $Y := a, b$. Then $P(Y) = 0.4 + 0.3 = 0.7$ and moreover
$$
P(a|Y) = P(a|Y)/P(Y)=0.4/0.7 = 4/7 > 1/2,
$$
which is what we were looking for.
answered Jul 16 at 17:34
AlgebraicsAnonymous
69111
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Ah, this is a problem regarding conditional probability. We define a probability space $Omega = a, b, c$, where
- $a$ means that the fund has beat the market,
- $b$ means that the fund has not beat the market, and the investors did not withdraw,
- and $c$ means that the fund has not beat the market, and the investors withdrew their money.
Now from the assumption, it follows that if $P$ is the probability measure, then $P(a) = 0.4$, and $P(X) = 0.6$, where $X = b,c$ is the event that the fund underperformed. Moreover,
$$
P(c|X) = 0.5 = P(b|X).
$$
But since $c cap X = c$ and $b cap X = b$, we may deduce from that that
$$
P(c) = P(b) = 0.5*0.6 = 0.3.
$$
Now note that the event that the fund still exists is $Y := a, b$. Then $P(Y) = 0.4 + 0.3 = 0.7$ and moreover
$$
P(a|Y) = P(a|Y)/P(Y)=0.4/0.7 = 4/7 > 1/2,
$$
which is what we were looking for.
answered Jul 16 at 17:34
AlgebraicsAnonymous
69111
add a comment |Â
up vote
1
down vote
accepted
Ah, this is a problem regarding conditional probability. We define a probability space $Omega = a, b, c$, where
- $a$ means that the fund has beat the market,
- $b$ means that the fund has not beat the market, and the investors did not withdraw,
- and $c$ means that the fund has not beat the market, and the investors withdrew their money.
Now from the assumption, it follows that if $P$ is the probability measure, then $P(a) = 0.4$, and $P(X) = 0.6$, where $X = b,c$ is the event that the fund underperformed. Moreover,
$$
P(c|X) = 0.5 = P(b|X).
$$
But since $c cap X = c$ and $b cap X = b$, we may deduce from that that
$$
P(c) = P(b) = 0.5*0.6 = 0.3.
$$
Now note that the event that the fund still exists is $Y := a, b$. Then $P(Y) = 0.4 + 0.3 = 0.7$ and moreover
$$
P(a|Y) = P(a|Y)/P(Y)=0.4/0.7 = 4/7 > 1/2,
$$
which is what we were looking for.
answered Jul 16 at 17:34
AlgebraicsAnonymous
69111
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Ah, this is a problem regarding conditional probability. We define a probability space $Omega = a, b, c$, where
- $a$ means that the fund has beat the market,
- $b$ means that the fund has not beat the market, and the investors did not withdraw,
- and $c$ means that the fund has not beat the market, and the investors withdrew their money.
Now from the assumption, it follows that if $P$ is the probability measure, then $P(a) = 0.4$, and $P(X) = 0.6$, where $X = b,c$ is the event that the fund underperformed. Moreover,
$$
P(c|X) = 0.5 = P(b|X).
$$
But since $c cap X = c$ and $b cap X = b$, we may deduce from that that
$$
P(c) = P(b) = 0.5*0.6 = 0.3.
$$
Now note that the event that the fund still exists is $Y := a, b$. Then $P(Y) = 0.4 + 0.3 = 0.7$ and moreover
$$
P(a|Y) = P(a|Y)/P(Y)=0.4/0.7 = 4/7 > 1/2,
$$
which is what we were looking for.
answered Jul 16 at 17:34
AlgebraicsAnonymous
69111
Ah, this is a problem regarding conditional probability. We define a probability space $Omega = a, b, c$, where
- $a$ means that the fund has beat the market,
- $b$ means that the fund has not beat the market, and the investors did not withdraw,
- and $c$ means that the fund has not beat the market, and the investors withdrew their money.
Now from the assumption, it follows that if $P$ is the probability measure, then $P(a) = 0.4$, and $P(X) = 0.6$, where $X = b,c$ is the event that the fund underperformed. Moreover,
$$
P(c|X) = 0.5 = P(b|X).
$$
But since $c cap X = c$ and $b cap X = b$, we may deduce from that that
$$
P(c) = P(b) = 0.5*0.6 = 0.3.
$$
Now note that the event that the fund still exists is $Y := a, b$. Then $P(Y) = 0.4 + 0.3 = 0.7$ and moreover
$$
P(a|Y) = P(a|Y)/P(Y)=0.4/0.7 = 4/7 > 1/2,
$$
which is what we were looking for.
answered Jul 16 at 17:34
AlgebraicsAnonymous
69111
edited Jul 16 at 17:56
answered Jul 16 at 17:34
AlgebraicsAnonymous
69111
answered Jul 16 at 17:34
AlgebraicsAnonymous
69111
answered Jul 16 at 17:34
AlgebraicsAnonymous
69111
69111
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