Most of us love Philippine mangoes but hate buying those tha

Most of us love Philippine mangoes, but hate buying those that are picked too early. Unfortunately, by waiting until the mangos are almost ripe to pick carries a risk of having 15% of the picked rot upon arrival at the packing facility. If the packing process is all done by machines without human inspection to pick out any rotten mangos, what would be the probability of having at most 2 rotten mangos packed in a box of 12?

Solution

n = 12

p = .15

1-p = .85

P(x) = C(n,x)p^x(1-p)^(n-x) = C(12,x).15^x(.85)^(12-x)

P(rotten mangoes <= 2) = P(0) + P(1) + P(2) =

C(12,0).15^0(.85)^(12-0) + C(12,1).15^1(.85)^(12-1) + C(12,2).15^2(.85)^(12-2) =

1*1*.85^12 + 12*.15*.85^11 + 66*.15^2*.85^10 = 0.73581808622345

Alternatively, from Excel, =BINOM.DIST(2,12,0.15,TRUE) = 0.73581808622345