X and Y are two events. The probability of X or Y is 0.7 and that of X is 0.4. If X and Y are independent, find the probability of Y.

  • A 0.30
  • B 0.50
  • C 0.57
  • D 1.80
jamb 2000mathematics

The correct answer is A. 0.30

Let's solve this problem together! If X and Y are two independent events, then the probability of X or Y is given by the formula P(X or Y) = P(X) + P(Y) - P(X)P(Y). We are given that P(X or Y) = 0.7 and P(X) = 0.4. Substituting these values into the formula above, we get:

\(0.7 = 0.4 + P(Y) - (0.4)(P(Y)) \)

\(0.7 = 0.4 + P(Y)(1 - 0.4) \)

\(0.3 = P(Y)(0.6) \)

\(P(Y)= \frac{0.3}{0.6} \)

\(P(Y)= 0.5\)

Therefore, the probability of event Y is 0.5.

Note, P(X)P(Y) will be zero if both events are mutually exclusive.

Previous question Next question