Question

A sample space S has two independent events, A and B, with Pr[A] = 0.36 and Pr[ A' n B'] = 0.48. Which of the following represents Pr [A n B'] ? A) 0.27 B) 0.09 C) 0.16 D) cannot be determined without more information E) none of the above. Also how do you get [A n B]?​

Answer 1

The probability of A intersection B' (Pr[A n B']) cannot be determined without more information, given that A and B are independent events with known probabilities.

Therefore, the correct answer is: option D) cannot be determined without more information.

Step-by-step explanation:

To find the probability of event A intersection B' (denoted as Pr[A n B']), we can use the formula P(A n B') = P(A) - P(A n B).

Since events A and B are independent, we know that P(A n B) = P(A) * P(B).

Given that Pr[A] = 0.36 and Pr[A' n B'] = 0.48, we can calculate P(A n B) as follows:

P(A' n B') = P(A') * P(B') = (1 - P(A)) * (1 - P(B))

= (1 - 0.36) * (1 - 0.3) = 0.64 * 0.7

= 0.448

P(A n B) = 1 - P(A' n B')

= 1 - 0.448

= 0.552

Finally, we can calculate P(A n B') using the formula P(A n B') = P(A) - P(A n B):

P(A n B') = P(A) - P(A n B)

= 0.36 - 0.552

= -0.192

Since probabilities cannot be negative, we can conclude that Pr[A n B'] cannot be determined without more information.