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?
A
\(\frac{4}{5}\)
B
\(\frac{3}{4}\)
C
\(\frac{3}{5}\)
D
\(\frac{1}{20}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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) = \(\frac{4}{5} \times \frac{3}{4} = \frac{12}{20}\)
= \(\frac{3}{5}\)
Source: Myschool Past Questions Archive (Record #36992)