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Conditional Probabilities on Hidden Prizes

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Need help with calculating probability. I have tried to solve the problems below, but I need you to give me step-by-step instructions to make sure that I understand how to do the problems correctly.

1. Use the information below to answer Items 10-11:
A game has three boxes. Box 1 has one drawer, Box 2 has two drawers, and Box 3 has three drawers. You will pick a box at random and then pick a drawer from that box at random.

a. A prize is hidden in the top drawer of Box 3. What is the probability that you select this drawer?
3/6=1/2 =0.5 or 50%

b. A prize is hidden in the only drawer of Box 1. What is the probability that you will select this drawer?
1/6 = 0.1667 or 16.67%

3. Consider a box game with 2 boxes. Box 1 has one drawer, and Box 2 has 5 drawers. A player will select a box at random and then pick a drawer from that box at random. You have two prizes to place in the drawers. Where should you place them to create the greatest probability that someone who plays the game will win a prize? Explain your reasoning.

I would place the prize in Box 2 because it has the most outcomes which gives the player more chances to select the drawer that containers the prize.

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Solution Summary

This solution shows step-by-step calculations to determine the conditional probabilities of selecting a hidden prize.

Solution provided by:
Robert Reinhart, MBA
Education
  • MBA, Merage School of Business, Univ of Cal, Irvine
  • BA, Univ of Cal, Irvine
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