In: Statistics and Probability
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?
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.