Question

The probability that a student owns a car is 0.65 and the probability that a student owns a computer is 0.82 if the probability that a student on owns both is 0.55 what is the probability that a given student owns A. A car or computer?B. A car or a computer but not both?C. A car given he had a computer?D. A computer given he had a car?E. Had both?

Answer 1

Let:

A = A student owns a car

B = A student owns a computer

so:

$\begin{gathered} P(A)=0.65 \\ P(B)=0.82 \\ P(A\cap B)=0.55 \end{gathered}$

a.

A car or computer:

$\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=0.65+0.82-0.55 \\ P(A\cup B)=0.92 \end{gathered}$

92%

b. A car or a computer but not both:

$\bar{P}(\bar{A}\cap\bar{B})=1-P(A\cap B)=1-0.55=0.45$

45%

c. A computer given he had a car?

$P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{0.55}{0.65}\approx0.85$

85%

d. Had both?

$P(A\cap B)=0.55$

55%