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Algebra Difficulty 1.6 Junior Find the answer Canada

Ben participates in a prize draw. He receives one prize that is equally likely to be worth $5,$ 10 or 20. Jamie participates in a different prize draw. She receives one prize that is equally likely to be worth 30 or 40. What is the probability that the total value of their prizes is exactly 50?

$\frac{1}{6}$
$\frac{1}{3}$
$\frac{1}{2}$
$\frac{2}{5}$
$\frac{2}{3}$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since there are two possible prizes that Jamie can win and each is equally likely, then the probability that Jamie wins $30 is$ $\frac{1}{2}$ and the probability that Jamie wins 40 is $\frac{1}{2}$ .

If Jamie wins 30, then for the total value of the prizes to be 50, Ben must win 20. The probability that Ben wins 20 is $\frac{1}{3}$ , since there are three equally likely outcomes for Ben.

If Jamie wins 40, then for the total value of the prizes to be 50, Ben must win 10. The probability that Ben wins 10 is $\frac{1}{3}$ .

Since Ben’s and Jamie’s prizes come from different draws, we can assume that the results are independent, and so the probability that Jamie wins $30 and Ben wins$ 20 is $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$ .

Similarly, the probability that Jamie wins $40 and Ben wins$ 10 is $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$ .

Therefore, the probability that the total value of their prizes is $50 is$ $\frac{1}{6} + \frac{1}{6} = \frac{1}{3}\$.$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.