Question

It is estimated that 75% of grapefruit crop is good; other 25% have rotten centers that cannot be detected until the grapefruit are cut open. The grapefruit are sold in sacks of 10.

Answer 1

Given

75% of grapefruit crop is good , p = 0.75

25% have rotten , q = 0.25

n = 10

Find

a) Probability of getting atleast 9 good grapefruit in a sack.

b) how many can you expect to be good in a sack.

Explanation

a) Probability of getting atleast 9 good grapefruit in a sack =

$\begin{gathered} P(X\ge9)=P(X=9)+P(X=10) \\ =^{10}C_9(0.75)^9(0.25)+^{10}C_{10}(0.75)^{10} \\ =0.18771171569+0.063135147 \\ =0.24402523039\approx0.24=24.4\% \end{gathered}$

b) expected number of grapefruit to be good =

$\begin{gathered} E(X)=n*p(X) \\ E(X)=10\times0.75 \\ E(X)=7.5 \end{gathered}$

Final Answer

Hence ,

a) Probability of getting atleast 9 good grapefruit in a sack is 24.4%

b) expected number of grapefruit to be good is 7.5