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The table gives a set of outcomes and their probabilities. Let  A be the event "the outcome is a divisor of 4". Let B

be the event "the outcome is prime". Find P(A|B)

Outcome Probability

1             0.1

2             0.6

3             0.2

4             0.1

Mar 5, 2023

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To find P(A|B), we need to find the probability of getting a divisor of 4 given that the outcome is prime.

First, we need to find P(B), the probability of getting a prime number. From the table, we see that the only prime number is 2, so P(B) = 0.6.

Next, we need to find P(A and B), the probability of getting a divisor of 4 and a prime number. The only outcome that satisfies both conditions is 2, so P(A and B) = 0.6.

Using Bayes' theorem, we have:

P(A|B) = P(A and B) / P(B)

Substituting the values we found, we get:

P(A|B) = 0.6 / 0.6 = 1

Therefore, the probability of getting a divisor of 4 given that the outcome is prime is 1 or 100%. This makes sense since the only prime number in the table is also a divisor of 4.

Mar 5, 2023