Question

Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram:

What is the probability of both events A and B occurring if P(A) = 0.6 and P(B) = 0.4, given that P(A ∩ B) = 0.2?

Answer 1

The probability of both events A and B occurring can be found using the formula P(A ∩ B) = P(A) × P(B|A), where P(A) = 0.6 and P(B) = 0.4.

Step-by-step explanation:

The probability of both events A and B occurring can be found using the formula P(A ∩ B) = P(A) × P(B|A), where P(A) = 0.6 and P(B) = 0.4. Given that P(A ∩ B) = 0.2, we can substitute the values into the formula to get:

P(A ∩ B) = 0.6 × P(B|A) = 0.2

Then, rearranging the formula, we have:

P(B|A) = 0.2 / 0.6 = 0.3333

So, the probability of both events A and B occurring is 0.3333.