Question

If you are randomly sampling without replacement from a jar containing 20 quarters, 16 dimes and 26 nickles what is the probability of obtaining:

a. exactly one dime in three draws?

b. exactly two nickles in three draws?

c. three nickels in three draws?

d. at least two quarters in three draws?

e. no quarters in three draws?

Answer 1

a.

Number of dimes = 16

Number of coins which are not dime = 20 + 26 = 46

Total Coins = 16 + 20 + 26 = 62

Number of ways to choose 3 coins from 62 coins =

= 37820

Number of ways to choose 1 dime from 16 dimes =

= 16

Number of ways to choose 2 Non-dime from 46 coins =

= 1035

probability of obtaining exactly one dime in three draws = Number of ways to choose 1 dime from 16 dimes * Number of ways to choose 2 Non-dime from 46 coins / Number of ways to choose 3 coins from 62 coins

= (16 * 1035) / 37820

= 0.4378636

b)

Number of nickles = 26

Number of coins which are not nickles = 20 + 16 = 36

Number of ways to choose 2 nickle from 26 nickles =

= 325

Number of ways to choose 1 Non-nickle from 36 coins =

= 36

probability of obtaining exactly two nickles in three draws = Number of ways to choose 2 nickle from 26 nickles * Number of ways to choose 1 Non-nickle from 36 coins / Number of ways to choose 3 coins from 62 coins

= (325 * 36) / 37820

= 0.3093601

c.

Number of ways to choose 3 nickle from 26 nickles =

= 2600

Number of ways to choose 0 Non-nickle from 36 coins =

= 1

probability of obtaining exactly two nickles in three draws = Number of ways to choose 2 nickle from 26 nickles * Number of ways to choose 1 Non-nickle from 36 coins / Number of ways to choose 3 coins from 62 coins

= (2600 * 1) / 37820

= 0.06874669

d.

Number of ways to choose 2 quarter from 20 quarters =

= 190

Number of ways to choose 1 Non-quarter from 42 coins =

= 42

probability of obtaining exactly two quarter in three draws = Number of ways to choose 2 quarter from 20 quarters * Number of ways to choose 1 Non-quarter from 42 coins / Number of ways to choose 3 coins from 62 coins

= (190 * 42) / 37820

= 0.2109995

Number of ways to choose 3 quarter from 20 quarters =

= 1140

Number of ways to choose 0 Non-quarter from 42 coins =

= 1

probability of obtaining exactly three quarter in three draws = Number of ways to choose 3 quarter from 20 quarters * Number of ways to choose 0 Non-quarter from 42 coins / Number of ways to choose 3 coins from 62 coins

= (1140 * 1) / 37820

= 0.03014278

probability of obtaining at least two quarter in three draws = 0.2109995 + 0.03014278 = 0.2411423

e.

Number of ways to choose 3 non-quarter from 42 coins =

= 11480

Number of ways to choose 0 quarter from 20 quarters =

= 1

probability of obtaining no quarters in three draws = Number of ways to choose 3 non-quarter from 42 coins * Number of ways to choose 0 quarter from 20 quarters / Number of ways to choose 3 coins from 62 coins

= (11480 * 1) / 37820

= 0.3035431