Answer: 1. 0.0256
2. 0.4096
Step-by-step explanation:
Binomial probability formula , to find the probability of getting x successes:
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex] , where n= Total number of trials
p= Probability of getting success in each trial.
Let x be the number of customers will make purchase.
As per given , we have
p= 0.20
n= 4
1. The probability that 3 of the next 4 customers will make a purchase will be:-
[tex]P(x=3)=^4C_3(0.20)^3(1-0.20)^{4-3}[/tex]
[tex]P(x=3)=(4)(0.20)^3(0.80)^{1}\ \ [\because\ ^nC_{n-1}=n][/tex]
[tex]P(x=3)=(4)(0.008)(0.80)=0.0256[/tex]
Hence, the probability that 3 of the next 4 customers will make a purchase = 0.0256
2. The probability that none of the next 4 customers will make a purchase will be :
[tex]P(x=0)=^4C_0(0.20)^0(1-0.20)^{4-0}[/tex]
[tex]P(x=0)=(1)(0.80)^{4}\ \ [\because\ ^nC_{0}=1][/tex]
[tex]P(x=0)=0.4096[/tex]
Hence, the probability that none of the next 4 customers will make a purchase= 0.4096
