A company offers a bonus to employees who complete certain training modules. The probability that Emma will complete the "Leadership Skills" module is 0.8, and the probability that John will complete the "Time Management" module is 0.5. What is the probability that both Emma and John will complete their respective modules?

Question: A company offers a bonus to employees who complete certain training modules. The probability that Emma will complete the "Leadership Skills" module is 0.8, and the probability that John will complete the "Time Management" module is 0.5. What is the probability that both Emma and John will complete their respective modules?

Solution:
Let,
Probability that Emma completes the "Leadership Skills" module P(E) = 0.8
P(J) = Probability that John completes the "Time Management" module P(J) = 0.5

Since the events are independent, the probability that both Emma and John will complete their respective modules,
P (E ∩ J) = P(E) × P (J)
= 0.8 × 0.5
= 0.4