Question

Kieran’s wallet contains 7 bills: three $5 bills, two $10 bills, one $20 bill, and one $100 bill. If Kieran pulls out two bills at random, what is the probability that he selects exactly two $5 bills? Use complete sentences to explain the probability. In your final answer, include all of your calculations.

Answer 1

Exact probability = 1/7

(Approximate probability = 0.142857)

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Step-by-step explanation:

There are three 5 dollar bills out of 7 total. The probability of selecting a five dollar bill is 3/7. Let A = 3/7 since we'll use it later.

After the first selection is made, we have 3-1 = 2 five dollar bills left out of 7-1 = 6 bills overall. This is assuming we do not put the first selection back, or replace it with another five dollar bill.

The probability of selecting another five dollar bill is 2/6 = 1/3. Let B = 1/3.

Multiply the values of A and B to get

A*B = (3/7)*(1/3) = (3*1)/(7*3)= 1/7

Note the 3's divide and cancel out.

Using a calculator, 1/7 = 0.142857 approximately

Answer 2

1/7

Step-by-step explanation:

$5 = 3, $10= 2, $20= 1, $100= 1- total 7 bills

• Probability of getting $5 bill is 3/7
• Probability of getting second $5 bill is 2/6= 1/3 as one of $5 bill already taken and total number of bills reduced to 6
• Probability of getting 2 of $5 bills is the product of individual probabilities: 3/7*1/3= 1/7

Answer is 1/7