Question

There are two events, A and B. If P(B) = 0.3, P(A|B) = 0.4 ,and P(B|A) = 0.5, what is P(A)? Ans: 1 A and B are two events from the same sample space, which satisfy P(A) =, P(B) and P(A U B) = 3. Compute the following probabilities. P(ANB) Ans: P(AB) Ans: • P(A n B") Ans: P(A|BC) Ans: For A, B are statistically independent events such that P(B) = 2 x P(A) and P(A U B) : Please find the value of P(A) and P(B). = Ans:

Answer 1

To find P(A) when given P(B), P(A|B), and P(B|A), we can use the formula P(A|B) = P(A ∩ B) / P(B). Rearrange the equation to solve for P(A), and substitute the given values to find P(A) = 0.4.

Step-by-step explanation:

P(A|B) represents the conditional probability of event A given that event B has already occurred. In this case, we are given P(A|B) = 0.4 and P(B|A) = 0.5. We need to find P(A). We can use the formula:

P(A|B) = P(A ∩ B) / P(B)

Substituting the given values, we have 0.4 = P(A ∩ B) / 0.3. Rearranging the equation, we get:

P(A ∩ B) = 0.4 * 0.3 = 0.12

Since P(A ∩ B) = P(A|B) * P(B), we can write:

P(A ∩ B) = P(A) * P(B)

Therefore, 0.12 = P(A) * 0.3. Solving for P(A), we find:

P(A) = 0.12 / 0.3 = 0.4