Question

Armando has some coins in his pocket. 3 dimes 2 quarters 2 pennies 5 nickles What is the probability that he will pull out a nickel, then a quarter, then a nickel if he does not put any of the coins back in his pocket after he selects it?

Answer 1

The probability that he will pull out a nickel, then a quarter, then a nickel is $\frac{1}{33}$

Explanation:

Given:

Number of dimes = 3

Number of Quarters = 2

Number of pennies = 2

Number of Nickles = 5

Total coins = 3 + 2 + 2 + 5

                 = 12  

Probability that Armando will pull out Nickel first = $\frac{5}{12}$                                                      

After taking out Nickel, the total number of coins in the pocket will be 11

So,

Probability that he will pull a quarter = $\frac{2}{11}$

Total coins remaining = 11 - 1 = 10

Total Nickel remaining = 5 - 1 = 4

Probability that he will take our Nickel = $\frac{4}{10} = \frac{2}{5}$

Total probability = $\frac{5}{12} X \frac{2}{11} X\frac{4}{10}$

                         = $\frac{1}{33}$