Question

A box of 6 coins (penny, nickel, dime or quarter) worth $0.67 is shaken. What is the probability that a nickel is drawn first and then a quarter? Assume no replacement and that all coins are equally likely.

Answer 1

The probability of pulling out a nickle would be 1/6
Drawing a quarter after would have a 2/5 chance
Multiply the two and the probability of that happening is 2/30
Simplify to 1/15

Answer 2

There is a 6.67% probability that a nickel is drawn first and then a quarter.

Explanation:

There are 6 coins. The sum of their values is $0.67. We need to find how many of each coin are there.

A penny is worth 1 cent.

A nickel is worth 5 cents.

A dime is worth 10 cents.

A quarter is worth 25 cents.

To get to 67 cents, we need:

Two pennies, a nickel, a dime and two quarters.

So:

What is the probability that a nickel is drawn first and then a quarter? Assume no replacement and that all coins are equally likely.

Initially there are 6 coins, of which 1 is a nickel. So the probability that the nickel is drawn is:

`P_(1) = (1)/(6)`

There are no replacements, so now there are 5 coins, of which 2 are quarters. So the probability that a quarter is drawn is:

`P_(2) = (2)/(5)`.

The probability that a nickel is drawn first and then a quarter is:

`P = P_(1)*P_(2) = (1)/(6){2}{5} = (1)/(15) = 0.0667`

There is a 6.67% probability that a nickel is drawn first and then a quarter.