Question

when randomly choosing two bills from a cup of bills that contains a $1 bill, a $2 bill, a $5 bill, a $10 bill, a $20 bill, and a $50 bill, what is the probability of choosing a $50 bill and a $20 bill? the probability of choosing a $50 bill and a $20 bill is (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the total number of ways to choose 2 bills

The total number of bills is \(n = 6\). The number of ways to choose 2 bills out of 6 is given by the combination formula \(C(n,k)=\frac{n!}{k!(n - k)!}\), where \(n = 6\) and \(k=2\).

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Step2: Calculate the number of ways to choose a $50 bill and a $20 bill

There is 1 way to choose the $50 bill and 1 way to choose the $20 bill. By the multiplication principle, the number of ways to choose a $50 bill and a $20 bill is \(1\times1 = 1\)

Step3: Calculate the probability

The probability \(P\) of an event is the number of favorable outcomes divided by the number of total outcomes. So \(P=\frac{1}{15}\)

Answer:

\(\frac{1}{15}\)