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# Peanut Probability

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A bag of peanuts in their shells contains 174 peanuts. 72 of the shells contain one peanut, 97 of the shells contain two peanuts, and the rest contain three peanuts. Of the shells with one peanut, 18 of them are cracked. Of the shells with two peanuts, 26 of them are cracked. None of the shells with three peanuts are cracked. One peanut shell is randomly selected from the bag.

What is the probability the shell is cracked?

What is the probability the shell is not cracked and it contains two peanuts?

What is the probability the shell is not cracked or it contains two peanuts?

What is the probability the shell is not cracked given that it contains two peanuts?

Jun 27, 2022

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Cracked           Not Cracked          Total

One Peanut                    18                      54                       72

Two Peanuts                   26                     71                       97

Three Peanuts                                           5                         5

________________________________

44                    130                     174

P(shell is  cracked )=  44 / 174 =    22 / 87

P(not cracked and  contains 2 peanuts)  = 71 / 174

P (not cracked or  contains 2 peanuts  ) =  P(not cracked) + P (2 peanuts) - P(not cracked and 2 peanuts)  =

(130) / 174   +  (97)/174  = (71) / 174 =   156 / 174  =  78 / 87  = 26 / 29

P not cracked given 2 peanuts)  =   71 / 97

Jun 27, 2022