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Given: P(A) = 35, P(B) = 250, and P(A ∩ B) = 20. Find P(A' ∩ B').

a. P(A' ∩ B') = 0
b. P(A' ∩ B') = 15
c. P(A' ∩ B') = 230
d. P(A' ∩ B') = 235

1 Answer

4 votes

Final answer:

The solution to finding P(A' ∩ B') requires clarification on the given probability values, as they are not within the typical range (0 to 1). The general formula for P(A' ∩ B') is applied by subtracting P(A), P(B), and adding P(A ∩ B) from the total probability, usually 1, but it's not feasible with the current values.

Step-by-step explanation:

The student is tasked with finding the probability of the complementary intersection between two events, labeled as P(A' ∩ B'). Given the probabilities of P(A) = 35, P(B) = 250, and the intersection of A and B is P(A ∩ B) = 20, we can use the formula for the probability of the complement of two intersecting events.

P(A' ∩ B') = Total probability - P(A) - P(B) + P(A ∩ B)

Assuming that the total probability represents all possible outcomes, it is typically equal to 1. However, the values given for P(A), P(B), and P(A ∩ B) appear unusually large for probabilities, as probabilities are typically between 0 and 1. Therefore, without additional information or clarification that the given values are indeed probabilities (but potentially atypical notations), the provided calculation cannot proceed accurately.

To find P(A' ∩ B') with typical probability values, the calculation would look like this:

P(A' ∩ B') = 1 - P(A) - P(B) + P(A ∩ B)

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