Answer: Probability both are nervous around strangers=0.04
Probability at least one is nervous around strangers = 0.36
Step-by-step 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 , [tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]
The probability both are nervous around strangers:-
[tex]P(x=2)=^2C_2(0.2)^2(0.8)^{0}=(0.2)^2=0.04[/tex]
The probability at least one is nervous around strangers :-
[tex]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[/tex]
