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
+195 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.
