Question

In: Statistics and Probability

A bag contains four quarters, one nickel, one dime, and five pennies. We reach with our...

  1. A bag contains four quarters, one nickel, one dime, and five pennies. We reach with our hand and pull out two coins at random. What are the chances that we pull $0.15 worth of coins?

Solutions

Expert Solution

solution : From the given

one Dime (D) =10 cents

one Nickel (N) = 5 cents

one Pennies (P) = 1 cent ( given 5 pennies )

one Quarter (Q)= 25 cents ( given 4 quarters)

given  four quarters, one nickel, one dime, and five pennies

we can make 15 cents using 1 Nickel and 1 Dime

we are drawing 2 coins randomly ,possibilities are,

1D , 1D = 1 * 0 = 0 possibilities

1N, 1N   = 1 * 0 = 0 possibilities

1P, 1P = 5 * 4 = 20 possibilities

1Q, 1Q = 4 * 3 = 12 possibilities

multiply below with 2, cause (1D, 1N) = (1N, 1D) these are 2 different possibilities

1D, 1N = 1 * 1 * 2 = 2 possibilities

1D, 1P = 1 * 5 * 2= 10 possibilities

1D, 1Q = 1 * 4 * 2= 8 possibilities

1N, 1P = 1 * 5 * 2 = 10 possibilities

1N, 1Q = 1 * 4 * 2= 8 possibilities

1P, 1Q = 5 * 4 * 2= 40 possibilities

possibilities that we are getting 0.15 dollars = 2

remaining possibilities = 20 +12 + 10 + 8 + 10 + 8 + 40 + 2 =110

probability that we get 0.15 dollars = 2/110 = 1/55 = 0.0181

which is 1.81 percent chances are there.


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