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# Probability

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I have a bag that contains 6 nickels and 5 pennies. I draw coins from the bag at random, without replacement. Find the probability that after drawing 4 coins, I have removed at most 2 pennies from the bag.

Feb 12, 2020

#2
+18974
+1

Since you have at most 2 pennies, you can have 0 pennies, 1 penny, or 2 pennies.

The number of ways to select 0 pennies and 4 nickels:  5C0 · 6C4

The number of ways to select 1 penny and 3 nickels:     5C1 · 6C3

The number of ways to select 2 pennies and 2 nickels:  5C2 · 6C2

Add those three answers to together and divide by the number of ways to select 4 coins from 11 coins:

The number of ways to select 4 coins from 11 coins:     11C4

Feb 13, 2020

#1
0

The probability is (24*1 + 18*2)/C(11,4) = 2/11.

Feb 12, 2020
#3
0

Guest Feb 13, 2020
#2
+18974
+1

Since you have at most 2 pennies, you can have 0 pennies, 1 penny, or 2 pennies.

The number of ways to select 0 pennies and 4 nickels:  5C0 · 6C4

The number of ways to select 1 penny and 3 nickels:     5C1 · 6C3

The number of ways to select 2 pennies and 2 nickels:  5C2 · 6C2

Add those three answers to together and divide by the number of ways to select 4 coins from 11 coins:

The number of ways to select 4 coins from 11 coins:     11C4

geno3141 Feb 13, 2020