Question

Suppose that 69% of people own fish. If you pick two people at random, what is the probability that they both own a fish?

Give your answer as a decimal at least 4 places.

Answer 1

p = probability of people who own fish = 0.69   ( 69 % is converted in to decimal )

n = random sample size = 2

x = 2   ( Both people own fish )

We use binomial distribution

$P(X=x) =\binom{n}{x}*p^x*(1-p)^{(n-x)}$

$P(X=2) =\binom{2}{2}*0.69^{2}*(1-0.69)^{(2-2)}$

$\binom{n}{x} = \frac{n!}{x!*(n-x)!}$

$\binom{2}{2} = \frac{2!}{2!*(2-2)!}$

$\binom{2}{2} = \frac{2!}{2!*(0)!}$

0! is always 1

2! = 2*1

$\binom{2}{2} = \frac{2*1}{2*1*1}$

$\binom{2}{2} = 1$

$P(X=2) = {\color{Purple} \boldsymbol{0.4761}}$

Final answer:-

The probability that they both own a fish = 0.4761