Question

Given that events A and B are independent with P(A) = 0.4 and P(B) = 0.25, determine the value of P(A and B), rounding to the nearest thousandth, if necessary.

a) 0.100
b) 0.150
c) 0.075
d) 0.160

Answer 1

The probability of events A and B both occurring, given that they are independent, is the product of their individual probabilities, which is 0.1.

Step-by-step explanation:

Since events A and B are independent, the probability of both events A and B occurring is the product of their individual probabilities. This is expressed mathematically as P(A and B) = P(A) × P(B). Given that P(A) = 0.4 and P(B) = 0.25, we find that P(A and B) = 0.4 × 0.25 = 0.1. Therefore, the value of P(A and B), rounded to the nearest thousandth if necessary, is 0.100.