Question

the table gives a set of outcomes and their probabilities. let a be the event \the outcome is less than 3\. let b be the event \the outcome is prime\. find p(a|b). outcome probability 1 0.5 2 0.4 3 0.1

Explanation:

Step1: Define event A and B

Event A: outcome < 3, so A = {1, 2}; Event B: outcome is prime, so B = {2, 3}. Then A ∩ B={2}.

Step2: Calculate P(A ∩ B)

The probability of outcome 2 is 0.4, so P(A ∩ B)=0.4.

Step3: Calculate P(B)

P(B)=P(2)+P(3)=0.4 + 0.1=0.5.

Step4: Use conditional - probability formula

The formula for conditional probability is P(A|B)=\frac{P(A\cap B)}{P(B)}. Substitute P(A ∩ B) = 0.4 and P(B)=0.5 into the formula.
P(A|B)=\frac{0.4}{0.5}=0.8

Answer:

0.8