**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) = \(\frac{4}{5} \times \frac{3}{4} = \frac{12}{20}\)

= \(\frac{3}{5}\)

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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) = \(\frac{4}{5} \times \frac{3}{4} = \frac{12}{20}\)

= \(\frac{3}{5}\)