Probability Addition Rule in Aptitude:

Overview:

Addition Rule of Probability:

If the probability of winning \(A\) is \(x\) and the probability of winning \(B\) is \(y\), then the probability that either \(A\) OR \(B\) wins will be, $$ \left[ P \ (A) + P \ (B) \right] $$ where as,

\(P \ (A)\) = Probability of \(A\) to win.

\(P \ (B)\) = Probability of \(B\) to win.

Addition Rule of Probability Examples:

Example (1): If the probability of \(p\) for winning a game of chess is \(\frac{5}{4}\) and the probability of \(q\) for winning the game is \(\frac{3}{4}\), then the probability that either \(p\) OR \(q\) wins the game of chess will be-

Solution: Given values, \(P \ (p) = \frac{5}{4}\) and \(P \ (q) = \frac{3}{4}\) then, $$ \left[ P \ (p) + P \ (q) \right] $$ $$ = \left[ \frac{5}{4} + \frac{3}{4} \right] = \frac{8}{4} = 2$$

Example (2): If the probability of John for winning the case of property is \(\frac{3}{5}\) and the probability of Jack for winning the case is \(\frac{1}{3}\), then the probability that either John OR Jack wins the case of property will be-

Solution: Given values, \(P \ (John) = \frac{3}{5}\) and \(P \ (Jack) = \frac{1}{3}\) then, $$ \left[ P \ (John) + P \ (Jack) \right] $$ $$ = \left[ \frac{3}{5} + \frac{1}{3} \right] = \frac{14}{15}$$

Example (3): If we have the probability of \(x\) winning a race as \(\frac{1}{2}\) and that of \(y\) as \(\frac{1}{3}\), then find the probability that eather \(x\) or \(y\) wins the race?

Solution: Given values, \(P \ (x) = \frac{1}{2}\)

\(P \ (y) = \frac{1}{3}\) then, $$ \left[ P \ (x) + P \ (y) \right] $$ $$ = \left[ \frac{1}{2} + \frac{1}{3} \right] = \frac{5}{6}$$