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


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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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