Final answer:
To find P(A ∩ B), use the formula P(A U B) = P(A) + P(B) − P(A ∩ B). With the given probabilities, P(A ∩ B) is calculated as 0.62 + 0.4 - 0.672, resulting in a probability of 0.348.
Step-by-step explanation:
The question is asking us to find the probability of the intersection of two events, which is denoted as P(A ∩ B). This can be calculated using the formula for the probability of the union of two events:
P(A U B) = P(A) + P(B) − P(A ∩ B). Rearranging this formula to solve for P(A ∩ B), we get:
P(A ∩ B) = P(A) + P(B) − P(A U B)
Given the values of P(A) = 0.62, P(B) = 0.4, and P(A U B) = 0.672, we plug these into the equation:
P(A ∩ B) = 0.62 + 0.4 − 0.672
P(A ∩ B) = 1.02 − 0.672
P(A ∩ B) = 0.348
Therefore, the value of P(A ∩ B), rounded to the nearest thousandth if necessary, is 0.348.