Answer:
The probability a person will not live in a mobile home if they do not die as a result of the tornado is 0.9265.
Step-by-step explanation:
Denote the events as follows:
X = a person lives in a mobile home.
Y = a person dies as a result of tornado.
Given:
[tex]P(X)=0.10\\P(Y|X) = 0.30\\P(Y|X^{c})=0.02\\[/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})\\=1-0.02\\=0.98[/tex]
Compute the probability that a person dies as a result of tornado as follows:
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})\\=(0.30\times0.10)+(0.02\times(1-0.10))\\=0.03+0.018\\=0.048[/tex]
Then the probability that a person does not dies as a result of tornado is:
[tex]P(Y^{c})=1-P(Y)\\=1-0.048\\=0.952[/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{0.98\times(1-0.10)}{0.952}=0.9265[/tex]
Thus, the probability a person will not live in a mobile home if they do not die as a result of the tornado is 0.9265.
