Sta301 GDB Solution 2016

Sta301 GDB 

Question: A man opens a general store and a book shop. In any one year the probability of a robbery in the general store is 0.10 and the probability of a robbery in the book shop is 0.02. For any one year. What is the probability that:

1. Neither business will be robbed.
2. Either one or the other (but not both) will be robbed.

Solution

Probability of a robbery in the general store = 0.10
probability of a robbery in the book shop = 0.02

P(A)=n(A)/n(S)

i. Neither business will be robbed.
P(A)=(not A)*(Not B)=(1-010)*(1-0.02)
P(A)=0.9*0.98=0.882


ii. Either one or the other (but not both) will be robbed.
P (B) = 0.10 + 0.02 - (0.10)(0.02)
P (B) = 0.12-0.002=0.118