Question

about 20% of the population of a large country is nervous around strangers. if two people are randomly selected , what is the probability both are nervous around strangers? what is the probability at least one is nervous around strangers?

Answer 1

The probability that both are nervous around strangers is (1/5)(1/5)=1/25

The probability that at least one is nervous around strangers is 1 - 1/25 = 24/25.

Answer 2

Answer: Probability both are nervous around strangers=0.04

Probability at least one is nervous around strangers = 0.36

Explanation:

Given : The probability of the population of a large country is nervous around strangers : p= 20%=0.20

Sample size : n=2

Let x be the number of success.

Using Binomial ,
`P(x)=^nC_xp^x(1-p)^(n-x)`

The probability both are nervous around strangers:-

`P(x=2)=^2C_2(0.2)^2(0.8)^(0)=(0.2)^2=0.04`

The probability at least one is nervous around strangers :-

`P(x\geq1)=1-P(x=0)\\\\=1-^2C_0(0.2)^0(0.8)^(2)\\\\1-(0.8)^2=1-0.64=0.36`