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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.

https://brainmass.com/statistics/probability-theory/conditional-probabilities-hidden-prizes-601361

#### Solution Summary

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

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## Statistics: Monty Hall problem, draw three kings, urns of red & green balls, radial tires

1. The Monty Hall problem is as follows: A contestant on a game show is given the opportunity to select one of three curtains on stage. One curtain hides a valuable prize and the other two hide worthless prizes. After the contestants selection, Monty, who knows what is behind each curtain, draws back one of the remaining curtains to show a worthless prize and offers the contestant the chance to exchange the selected curtain for the one remaining. Should the contestant keep the curtain originally selected or exchange it for the remaining? Verfiy your answer using probabilities.

2. You have a standard deck of cards and draw five cards at random. What is the probability you draw three kings?

3. Supppose you have two urns, each containing red and green balls. THe first urn contains 7 red and 3 green balls and the second urn contains 4 red and 5 green balls. Suppose now that you randomly select a ball from the first urn and place it (unseen) into the second urn. You then randomly select a ball from the second urn.
a. What is the probability that the ball you selected from the second urn is green?
b. What is the probability that the ball you selected from the second urn is green, given that the ball selected from the first urn was red?

4. A sales representative for a tire manufacture claims that the companies steel-belted radials get at least 35,000 miles. A tire dealer decides to check this claim by testing eight of the tires. If 75% or more of the eight tires he tests get at least 35,000 miles, he will purchase tires from the representative. IF, in fact, 90% of the steel-belted radials get at least 35,000 miles, what is the probability that the tire dealer purchases tires from the sales representative?

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