A bakerman sells 5 types of cakes. Profit due to the sale of each type of cake is respectively Rs3, Rs 2.5, Rs 2, Rs 1.5, Rs 1. The demands for these cakes are `10%, 5%, 25%, 45% and 15%` respectively.. What is he expected profit per cake?

Explanation

Let x be the profit due to sale of the cake.
Then x take the value 3, 2.5, 1.5, 1
`therefore" "=P(x=3)=10%=(10)/(100)`
`" "P(x=2.5)=5%=(5)/(100)`
`" "P(x=2)=25%=(25)/(100)`
`" "P(x=1.5)=45%=(45)/(100)`
`" "P(x=1)=15%=(15)/(100)`
`therefore" "` The probability distribution of x is as below.

`therefore" "` Expected profit per cake
`E(x)=Sigma x.P(x)`
`=3xx(10)/(100)+2.5xx(5)/(100)+2xx(25)/(100)+1.5xx(45)/(100)+1xx(15)/(100)`
`=(30)/(100)+(12.5)/(100)+(50)/(100)+(67.5)/(100)+(15)/(100)`
`=(175)/(100)="Rs. 1.75"`