Question

Suppose that A and B be two events defined on a sample space

Ω
with P(A) = 0.7, P(Bc | A) = 0.8 and P(B | Ac
)= 0.4
A) Find P(Ac)
B) Find P(B | A)
C) Find P(A ∩ B)
D) Find P(B)
E) Find P( A | B)

Answer 1

P(Ac) = 0.3, P(B | A) and P(A ∩ B) cannot be calculated without additional information, P(B) cannot be calculated without the value of P(B), P( A | B) cannot be calculated without additional information.

Step-by-step explanation:

A) Find P(Ac)

P(Ac) is the probability of the complement of event A, which is the probability of not A. Since A and not A are mutually exclusive and exhaustive events, P(Ac) can be found by subtracting P(A) from 1. Therefore, P(Ac) = 1 - P(A) = 1 - 0.7 = 0.3.

B) Find P(B | A)

P(B | A) is the conditional probability of event B given event A. It can be found using the formula: P(B | A) = P(A ∩ B) / P(A). We don't have the value of P(A ∩ B), so we cannot calculate P(B | A) without additional information.

C) Find P(A ∩ B)

P(A ∩ B) is the probability of the intersection of events A and B. We don't have the value of P(A ∩ B), so we cannot calculate it.

D) Find P(B)

P(B) is the probability of event B. We don't have the value of P(B), so we cannot calculate it.

E) Find P( A | B)

P( A | B) is the conditional probability of event A given event B. We don't have enough information to calculate P( A | B).