# Statistics: Probability of Die Rolls

A 6-sided die is rolled and depending on the result a ball is then chosen from one of three boxes. If the roll results in a 1 a ball is drawn from box A, if the roll results in a 2 or a 3 a ball is drawn from box B, and if the roll results in a 4, 5, or 6 a ball is drawn from box C. If box A contains 1 red, 6 white, and 3 black balls, box B contains 6 red and 4 black balls, and box C contains 3 white and 7 black balls:

a) What is the probability that you draw a black ball?

b) What is the probability that you draw a red ball from box A?

c) What is the probability that you draw a black ball that does not come from box B?

d) What is the probability that you draw a white ball given that you drew the ball from box C?

e) What is the probability that you drew from box A given that the ball is black?

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#### Solution Preview

The setup of the question can be summarized as follows.

Let X be the number that appears on the fair 6-sided die.

X = 1 ----> A (1 red, 6 white, 3 black)

X = 2,3 ----> B (6 red, 4 ...

#### Solution Summary

This solution assists with the probability problems attached regarding die rolls.

4 Problems Statistics: random selection, die or coin roll, safety or seat belt use

1) A container contains 3 slips of paper numbered 1, 2, and 3 respectively. A slip is randomly selected and replaced and then another slip is randomly selected. If A is the event that the same number is drawn each time, how many outcomes are in the event not A?

2) If you rolled a die. What would be the probability that a 1 or 3 is rolled?

3) If a coin is tossed and a die is rolled, what is the probability that a tails is tossed and a 5 is rolled?

4) A survey was taken to see whether males or females are more likely to wear safety belts. The survey consisted of 1,000 males and 1,000 females

Wears seat belt Male Female Total

Yes 824 681 1505

No 176 319 495

Total 1,000 1,000 2,000

a) Given that the respondent wears a seat belt, what is the probability that the person is a Male?

b) Given that the respondent is a Male, what is the probability that he wears a seatbelt?

c) Are the two events from a) and b) statistically independent?

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