Question

For all parts of this problem, P(Ā)=0.75 , P(B)=0.3 , and P(B∣A)=0.15

12. Compute P(A and B). Express your answer as a decimal.


13. Compute P(A or B). Express your answer as a decimal.

Answer 1

12. I assume
`\bar A` denotes the complement of A, so

`P(A) = 1 - P(\bar A) = 0.25`

Then by definition of conditional probability,

`P(B\mid A) = (P(A\cap B))/(P(A)) = (P(A\cap B))/(0.25) = 0.15 \\\\ \implies \boxed{P(A\cap B) = 0.0375}`

13. By inclusion/exclusion,

`P(A\cup B) = P(A) + P(B) - P(A\cap B) = 0.25 + 0.3 - 0.0375 \\\\ \implies \boxed{P(A\cup B) = 0.5125}`