Illinois State University Mathematics Department

MAT 312: Probability and Statistics for Middle School Teachers

Dr. Roger Day (day@ilstu.edu)



Probability Problems
look at possible solutions


Consider the experiment of selecting a card from an ordinary deck of 52 playing cards. Determine the probability of each outcome.

1.

A face card is drawn.

2.

A red card or a card showing a 5 is drawn.

3.

A non-face card or a 7 is drawn.

4.

A card drawn is neither a king nor a spade.

5.

A card that is a black face card is drawn.

6.

A card that is not a face card is drawn.

A box contains three red balls and two white balls. A ball is selected at random from the box, its color is recorded, and the ball is replaced. A second ball is then selected at random and its color is recorded. The outcome associated with this type of selection is an ordered pair (first drawn second draw). An example outcome is (red,white).

7.

List the sample space for this experiment.

8.

Determine the probability that both balls are red.

9.

Determine the probability that both balls are white.

10.

Explain why the probabilities determined for (8) and (9) do not sum to 1.

The table of information was recently collected at the Jamestown School dining hall.

Use this information to calculate the probabilities indicated for someone picked at random from the school's student population.

Class

Males

Females

9th grade

91

101

10th grade

95

105

11th grade

103

98

12th grade

97

101

11.

P(male)

12.

P(10th grader)

13.

P(male | 9th grader)

14.

P(9th grader | male)

15.

P(junior or senior)

16.

P(11th grader and female)


17.

Suppose we know that for event A, P(A) = 0.65. If ~A represents the event complementary to A, what is P(~A)?

18.

An experiment has three possible outcomes, X, Y, and Z. If P(Z) = P(X) and P(Y) = 3·P(X), determine P(X), P(Y), and P(Z).

A family has three children, ages 5, 7, and 10. If we assume that the probability of giving birth to a boy is the same as the probability of giving birth to a girl, determine the following probabilities.

19.

P(three girls)

20.

P(at least two boys)

21.

P(the oldest is a girl)

22.

P(two children are of the same gender)

23.

P(there are an equal number of boys and girls)

Three different gaming machines were on exhibit at a local casino. A sign on each machine showed its sample space (in dollars) and the probability of each guaranteed output in the sample space.

24.

If you wanted to select the machine that produced the largest average (mean) output over a long time period, which machine would you select? Explain.

25.

Suppose that you and two friends are beginning to play the three machines. If you have first choice on which machine you'll play, which of the three would you choose? Explain.


26.

A fair die is rolled three consecutive times. What is the probability that the digit sum of the three rolls is 15 or larger?

27.

A fair die is rolled six times. Determine the probability that each of the six equally likely outcomes appears exactly once in those six rolls.

A production line is equipped with two quality-control check points that tests all items on the line. At check point #1, 10% of all items failed the test. At check point #2, 12% of all items failed the test. We also know that 3% of all items failed both tests.

28.

If an item failed at check point #1, what is the probability that it also failed at check point #2?

29.

If an item failed at check point #2, what is the probability that it also failed at check point #1?

30.

What is the probability that an item failed at check point #1 or at check point #2?

31.

What is the probability that an item failed at neither of the check points?

George knows that a rare disease, D, within his family can be passed on to his children, and that the probability is 0.10 that the inherited disease will be passed on to a child. We signify this at P(D) = 0.10.

32.

Determine the probability that none of George's three children inherit the disease from George.

33.

If P(D) = x, determine the largest value of x possible so that the solution to (32) would be greater than or equal to 90%.

Suppose the Atlanta Braves and the New York Yankees meet in the next Major League Baseball World Series, where the two teams play until one team has won four games. Let B represent the event that the Braves win a game and let Y represent the event that the Yankees win a game, with P(B) = 0.4 and P(Y) = 0.6). Assume that these probabilities do not change throughout the series. Determine the following probabilities for this World Series.

34.

P(Atlanta wins no games)

35.

P(series is tied 2 games each after the first 4 games)

36.

P(the series ends in 5 games)

37.

P(if the series lasts 7 games, Atlanta will win)