# Probability Addition Rule in Aptitude:

#### Overview:

 Topic Included: Formulas, Definitions & Exmaples. Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Probability Aptitude Notes & Questions. Questions for practice: 10 Questions & Answers with Solutions.

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