Question

In Australia, 16% of the adult population is near-sighted. If three Australians are chosen at random, what is the probability that (a) two are nearsighted and one is not

Answer 1

Probabilities are used to determine the chances of events

The probability that  two are nearsighted and one is not, is 0.0645

How to determine the probability

The given parameters are:

n = 3 -- the number of Australians selected

r = 2 --- the number that are nearsighted

p = 16% --- the proportion that are nearsighted.

The probability that  two are nearsighted and one is not, is calculated using the following binomial probability formula

$P(x = r) = ^nC_r * p^r * (1 -p)^{n-r}$

So, we have:

$P(x = 2) = ^3C_2 * (16\%)^2 * (1 -16\%)^{3-2}$

$P(x = 2) = 0.0645$

Hence, the probability that  two are nearsighted and one is not, is 0.0645

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