A bag of peanuts in their shells contains 178 peanuts. 78 of the shells contain one peanut, 95 of the shells contain two peanuts, and the rest contain three peanuts. Of the shells with one peanut, 19 of them are cracked. Of the shells with two peanuts, 25 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?

0.507 (rounded off to 3 decimal places)

Step-by-step explanation:

Shells that contain 1 peanut=78

Cracked shells= 19 out of 78

To calculate probability we will divide the number of peanuts with cracked shells by the total number of shells having one peanut.

we get probability=

Shells that contain 2 peanuts=95

Cracked shells= 25

To calculate probability we will divide the number of peanuts with cracked shells by the total number of shells having two peanuts.

we get probability=  

We can calculate the number of shells containing 3 peanuts and find out its probability but it is unnecessary as there are no cracked shells and anything divided by 0 is 0.

we get probability=0

The final probability that the shell is cracked will be the sum of the three probabilities we found earlier.

= 0.507 (rounded off to 3 decimal places)

step-by-step explanation:

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