# Probability Multiplication 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.

#### Multiplication Rule of Probability:

If the probability of winning $$A$$ is $$x$$ and the probability of winning $$B$$ is $$y$$, then the probability of winning $$A$$ AND $$B$$ both.$$\left[ P \ (A) \times P \ (B) \right]$$ where as,

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

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

#### Multiplication Rule of Probability Examples:

Example (1): If the probability of $$p$$, winning a game is $$\frac{5}{4}$$ and the probability of $$q$$, winning is $$\frac{4}{3}$$, then the probability of winning $$p$$ AND $$q$$ both-

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

Example (2): If the probability of passing in an exam is $$\frac{2}{3}$$ for $$x$$ and the probability of passing the same exam is $$\frac{4}{3}$$ for $$y$$, then the probability of passing $$x$$ AND $$y$$ both will be-

Solution: Given values, $$P \ (x) = \frac{2}{3}$$ and $$P \ (y) = \frac{4}{3}$$ then, $$\left[ P \ (x) \times P \ (y) \right]$$ $$= \left[ \frac{2}{3} \times \frac{4}{3} \right] = \frac{8}{9}$$

Example (3): If the balls are not being replaced, then find the chance of drawing $$2$$ Red balls in succession from a bag containing $$7$$ Blue and $$3$$ Red balls?

Solution: Probability of getting Red balls in first draw = $$\frac{3}{10}$$

Probability of getting Red balls in second draw = $$\frac{2}{9}$$ then, $$P = \left[ \frac{3}{10} \times \frac{2}{9} \right] = \frac{1}{15}$$