Question

59% of the working population attended college. If a person in the working population attended college, there is a 0.94 probability the person is currently employed. If a person did not attend college, there is a 0.89 probability the person is currently employed. What is the probability a person did not attend college if the person is not currently employed

Answer 1

Answer:

The probability that a person did not attend college if the person is not currently employed is 0.5602.

Step-by-step explanation:

Denote the events as follows:

X = a person attended college

Y = a person is employed.

Given:

$P(X)=0.59\\P(Y|X)=0.94\\P(Y|X^{c})=0.89$

Compute the value of $P(Y^{c}|X^{c})$ as follows:

$P(Y^{c}|X^{c})=1-P(Y|X^{c}) = 1 - 0.89=0.11$

Compute the probability of a person being employed as follows:

$P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})\\=(0.94\times0.59)+(0.89\times(1-0.59))\\=0.5546+0.3649\\=0.9195$

Then the value a person being not employed is:

$P(Y^{c})=1-P(Y)=1-0.9195=0.0805$

Compute the value of $P(X^{c}|Y^{c})$ as follows:

$P(X^{c}|Y^{c})=\frac{P(Y^{c}|X^{c})P(X^{c})}{P(Y^{c})}=\frac{0.11\times(1-0.59)}{0.0805}=0.5602$

Thus, the probability that a person did not attend college if the person is not currently employed is 0.5602.