Question

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 22 Pennies 27 Dimes 9 Nickels 30 Quarters What is the probability that you reach into the jar and randomly grab a penny and then, without replacement, a dime

Answer 1

`P(Penny\ and\ Dime) = (9)/(116)`

Explanation:

Given

`Pennies = 22`

`Dimes = 27`

`Nickels = 9`

`Quarters = 30`

Required

`P(Penny\ and\ Dime)`

This is calculated as:

`P(Penny\ and\ Dime) = P(Penny) * P(Dime)`

Since it is a selection without replacement, the computation is:

`P(Penny\ and\ Dime) = (Penny)/(Total) * (Dime)/(Total-1)`

So, we have:

`P(Penny\ and\ Dime) = (22)/(22+27+9+30) * (Dime)/(22+27+9+30-1)`

`P(Penny\ and\ Dime) = (22)/(88) * (27)/(87)`

`P(Penny\ and\ Dime) = (1)/(4) * (9)/(29)`

`P(Penny\ and\ Dime) = (9)/(116)`