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:
[tex]P(X)=0.59\\P(Y|X)=0.94\\P(Y|X^{c})=0.89[/tex]
Compute the value of [tex]P(Y^{c}|X^{c})[/tex] as follows:
[tex]P(Y^{c}|X^{c})=1-P(Y|X^{c}) = 1 - 0.89=0.11[/tex]
Compute the probability of a person being employed as follows:
[tex]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[/tex]
Then the value a person being not employed is:
[tex]P(Y^{c})=1-P(Y)=1-0.9195=0.0805[/tex]
Compute the value of [tex]P(X^{c}|Y^{c})[/tex] as follows:
[tex]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[/tex]
Thus, the probability that a person did not attend college if the person is not currently employed is 0.5602.
