Question

18) For an environmental group, it is known that 75% of their door-to-door solicitations result in a donation of some kind. Find the probability that...
a) ...of the next 5 visits, at least 3 will be refusals.

b) ...3 of the next 5 visits will result in donations.

c) ...the first refusal will occur on the fifth visit.

d) ...the second refusal will occur on the fifth visit.

e) ...the third donation will be made on the fifth visit.

Answer 1

18)

a)P( .of the next 5 visits, at least 3 will be refusals )=P(at most 2 donation)

=P(X=0)+(X=1)+P(X=2)=⁵C₀(0.75)⁰(0.25)⁵+⁵C₁(0.75)¹(0.25)⁴+⁵C₂(0.75)²(0.25)³=0.1035

b)

3 of the next 5 visits will result in donations=⁵C₃(0.75)³(0.25)² =0.2637

c)

.the first refusal will occur on the fifth visit =(0.75)⁴*0.25=0.0791

d)

the second refusal will occur on the fifth visit =P(exactly 1 refusal in first 4 attempt and 2nd refusal on 5th attempt)=⁴C₁(0.25)²(0.75)³ =0.1055

e) .the third donation will be made on the fifth visit

=P(exactly 2 donation in first 4 attempt and 3rd donation on 5th attempt)

=⁴C₂(0.75)³(0.25)² =0.1582