Question

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 18 Pennies13 Dimes 18 Nickels13 Quarters What is the probability that you reach into the jar and randomly grab a nickel and then, without replacement, another nickel

Answer 1

`P(Nickel\ and\ Nickel) = 0.08091`

Explanation:

Given

`Pennies = 18`

`Dimes = 13`

`Nickels = 18`

`Quarters = 13`

Required

Probability of selecting 2 nickels without replacement

This can be represented as:
`P(Nickel\ and\ Nickel)`

The solution is as follows

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

The second nickel is reduced by 1 because the first nickel was not replaced and this also reduces the total by 1

So, we have:

`P(Nickel\ and\ Nickel) = (18)/(62)*(18-1)/(62-1)`

`P(Nickel\ and\ Nickel) = (18)/(62)*(17)/(61)`

`P(Nickel\ and\ Nickel) = (18*17)/(62*61)`

`P(Nickel\ and\ Nickel) = (306)/(3782)`

`P(Nickel\ and\ Nickel) = 0.08091`