(23) There are 10 boxes in a grab bag. The
boxes are identical except that 7 of
them contain bills. A contest winner
gets to pick fwo boxes from the grab
bag. What is the probability of getting
two bills?

Question

(23) There are 10 boxes in a grab bag. The
boxes are identical except that 7 of
them contain

bills. A contest winner
gets to pick fwo boxes from the grab
bag. What is the probability of getting
two

bills?

UpStudy AI · Accepted Answer

We start by finding the total number of ways to pick 2 boxes from 10, which is given by the combination formula:
$$
\binom{10}{2} = \frac{10 \times 9}{2 \times 1} = 45.
$$

Next, we determine the number of favorable ways to pick 2 boxes that each contain a $$\$20$$ bill. Since there are 7 boxes with $$\$20$$ bills, the number of ways to choose 2 of these is:
$$
\binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21.
$$

The probability of selecting 2 boxes with $$\$20$$ bills is the number of favorable outcomes divided by the total number of outcomes:
$$
P = \frac{\binom{7}{2}}{\binom{10}{2}} = \frac{21}{45}.
$$

This fraction simplifies by dividing the numerator and denominator by 3:
$$
\frac{21 \div 3}{45 \div 3} = \frac{7}{15}.
$$

Thus, the probability of getting two $$\$20$$ bills is $$\boxed{\frac{7}{15}}$$.
The probability of getting two \$20 bills is $$\frac{7}{15}$$.

(23) There are 10 boxes in a grab bag. The
boxes are identical except that 7 of
them contain bills. A contest winner
gets to pick fwo boxes from the grab
bag. What is the probability of getting
two bills?

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(23) There are 10 boxes in a grab bag. The boxes are identical except that 7 of them contain bills. A contest winner gets to pick fwo boxes from the grab bag. What is the probability of getting two bills?

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Latest Probability Questions

(23) There are 10 boxes in a grab bag. The
boxes are identical except that 7 of
them contain bills. A contest winner
gets to pick fwo boxes from the grab
bag. What is the probability of getting
two bills?