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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
Week in Review, Sections 7.2-7.4
1. A pair of fair dice is rolled, and the numbers rolled are recorded.
(a) Is the sample space uniform? Why or why not?
(b) Calculate the probability that the product of the two numbers rolled is 6 or 8.
(c) Calculate the probability that the product of the numbers is 4 or the sum of the numbers
is 4.
2. A bag of Skittles contains 13 yellow, 11 green, 9 orange, 6 red, and 5 purple. I reach in and
pull out one Skittle.
(a) What is the probability distribution for this experiment?
(b) Calculate the probability that I will get a green or an orange.
(c) Calculate the probability that I will not get a purple.
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
3. Suppose P (E c ) = .6, P (F ) = .5, and P (E ∪ F ) = .6. Calculate the following.
(a) P (E ∩ F )
(b) P (F c )
(c) P (E c ∪ F c )
(d) P (E c ∩ F )
4. 500 people were surveyed about what Oscar-nominated movies they had seen. 264 of them had
seen The Departed while 175 of them had seen Babel. 150 people had seen neither. What is
the probability that a person selected at random from this group
(a) Had seen both?
(b) Had seen The Departed but not Babel ?
(c) Had seen at least one of these two movies?
(d) Had not seen Babel ?
5. A committee of three people is to be randomly selected from a group of five women and seven
men. What is the probability that the committee will be:
(a) Comprised entirely of women.
(b) Not comprised entirely of women.
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
6. In the game of Rummikub, there are 52 tiles. The tiles are divided into four colored sets,
each consisting of the numbers 1 through 13. The four colors are blue, black, red, and orange.
Suppose that all the tiles are put into a bag and one tile is selected at random. Calculate the
probability that
(a) A red or black tile is selected.
(b) A blue tile is not selected.
(c) An orange tile or a 9 is selected.
(d) Neither a black tile nor a 12 is selected.
7. Two sisters compete in a race with five friends. The racers draw lots to determine their starting
positions. What is the probability that
(a) the older sister starts in lane 1 and the younger sister starts in lane 2?
(b) the two sisters compete next to each other?
8. If ten fair coins fall to the floor, what is the probability that there are five heads and five tails?
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
9. Two dice, one red and one white, are tossed. What is the probability that the white die turns
up a larger number than the red die.
10. If four dice are thrown, what is the probability that the four numbers turning up will be all
different?
11. If seven dice are thrown, what is the probability that exactly three 6’s will turn up?
12. A teacher is going to separate ten boys into two teams of five each to play basketball by drawing
five names out of a hat containing all ten names. As the drawing is about to start, one boy
says to a good friend, “I hope we get on the same team.” His friend replies, “Well, we have a
fifty-fifty chance.” Is he right, in the sense that the probability that the two boys will be on
the same team is 1/2?
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
13. The letters of the alphabet are written in random order. What is the probability that x and y
are adjacent?
14. What is the probability that four cards dealt at random from an ordinary deck of 52 cards will
contain one from each suit, that is to say, one heart, one spade, one club and one diamond?
15. Find the probability that when 13 cards are dealt from an ordinary deck of 52 cards
(a) at least two are face cards;
(b) exactly one ace is present;
(c) at least one ace is present.
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Problems 8-15 have been selected from the book “Mathematics of Choice, or How to Count without Counting” by
Ivan Niven.
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
16. (Birthday Problem) Suppose 23 unrelated people are gathered together and that each person
has an equal probability of being born on any day of the calendar year. Assuming that a
calendar year has 365 days, what is the probability that we will find two or more people in the
gathering with the same birthday?
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