Question

The US Postal Service reports 88% of first-class mail within the same city is delivered within 1 day of the time of mailing. Five letters are randomly send to different local addresses. What is the probability that:

a.) All five arrive within 1 day

b.) Exactly 4 arrive within 1 day

Answer 1

The US Postal Service reports 88% of first-class mail within the same city is delivered within 1 day of the time of mailing.

let X denotes the number of letters arriving within 1 day among the 5 letters randomly send.

then X~Bin(5,0.88)

so pmf of X is P[X=x]=⁵C_x(0.88)^x(1-0.88)^5-x x=0,1,2,3,4,5

a) so the probability that all 5 arrive within 1 day,

is P[X=5]=⁵C₅(0.88)⁵(1-0.88)^5-5=0.88⁵=0.5277 [answer]

b) so the probability that exactly 4 arrive within 1 day,

is P[X=4]=⁵C₄(0.88)⁴(1-0.88)^5-4=5*(0.88)⁴(0.12)=0.3598 [answer]