The probability of an event P is \(\frac{3}{4}\) while that of another event Q is \(\frac{1}{6}\). If the probability of both P and Q is \(\frac{1}{2}\). What is the probability of either P or Q.

  • A \(\frac{1}{96}\)
  • B \(\frac{1}{8}\)
  • C \(\frac{5}{6}\)
  • D \(\frac{11}{12}\)
jamb 1992mathematics

The correct answer is D. \(\frac{11}{12}\)

The probability of either event P or event Q occurring is given by the formula: P(P or Q) = P(P) + P(Q) - P(P and Q). Substituting the given probabilities into this formula, we get:

P(P or Q) = P(P) + P(Q) - P(P and Q)

= \(\frac{3}{4}\) + \(\frac{1}{6}\) - \(\frac{1}{2}\)

= \(\frac{9}{12}\) + \(\frac{2}{12}\) - \(\frac{6}{12}\)

= \(\frac{11}{12}\)

Previous question Next question