Question

A bag contains 5 nickels, 7 dimes, and 4 quarters. if you draw 3 coins at random from the bag, without replacement, what is the probability that you will get a nickel, a quarter, and a nickel, in that order? (enter your probability as a fraction.)

Answer 1

The probability of drawing a nickel, then a quarter, and then another nickel, in that order, is
`\( (1)/(42) \)`.

The probability of drawing a nickel, then a quarter, and then another nickel can be calculated step by step:

First, determine the probability of drawing a nickel on the first draw: There are 5 nickels out of a total of 16 coins, so the probability is
`\( (5)/(16) \).`

After drawing one nickel, there are now 4 nickels and 15 coins remaining. The probability of drawing a quarter on the second draw is
`\( (4)/(15) \)`.

Finally, after drawing a nickel and a quarter, there are 14 coins left with 4 nickels. The probability of drawing a nickel on the third draw is
`\( (4)/(14) = (2)/(7) \)`.

To find the overall probability of getting a nickel, then a quarter, and then another nickel, you multiply the individual probabilities together:

`\((5)/(16) * (4)/(15) * (2)/(7) = (40)/(1680) = (1)/(42)\)`