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# The probability of an event P happening is $$\frac{1}{5}$$ and that of events ar...

### Question

The probability of an event P happening is $$\frac{1}{5}$$ and that of events are independent, what is the probability that neither of them happens?

### Options

A) $$\frac{4}{5}$$

B) $$\frac{3}{4}$$

C) $$\frac{3}{5}$$

D) $$\frac{1}{20}$$

The correct answer is C.

### Explanation:

Prob(P) = $$\frac{1}{5}$$
Prob(Q) = $$\frac{1}{4}$$
Prob(neither p) = 1 - $$\frac{1}{5}$$
$$\frac{5 - 1}{5} = \frac{4}{5}$$
Prob(neither Q) = 1 - $$\frac{1}{4}$$
$$\frac{4 - 1}{4} = \frac{3}{4}$$
Prob(neither of them) = $$\frac{4}{5} \times \frac{3}{4} = \frac{12}{20}$$
= $$\frac{3}{5}$$

## Dicussion (1)

• Prob(P) = $$\frac{1}{5}$$
Prob(Q) = $$\frac{1}{4}$$
Prob(neither p) = 1 - $$\frac{1}{5}$$
$$\frac{5 - 1}{5} = \frac{4}{5}$$
Prob(neither Q) = 1 - $$\frac{1}{4}$$
$$\frac{4 - 1}{4} = \frac{3}{4}$$
Prob(neither of them) = $$\frac{4}{5} \times \frac{3}{4} = \frac{12}{20}$$
= $$\frac{3}{5}$$

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