The probability of an event P happening is $\frac{1}{5}$ and that of event Q is $\frac{1}{4}$ . If the events are independent, what is the probability that neither of them happens?

$\frac{4}{5}$

$\frac{3}{4}$

$\frac{3}{5}$

$\frac{1}{20}$

Correct answer is C

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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