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?
+128408 Cracked Not Cracked Total
One Peanut 18 54 72
Two Peanuts 26 71 97
Three Peanuts 5 5
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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
