Math 141 WIR7_Dr. Rosanna Pearlstein: Use of Counting Techniques in Probability
1. Two cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability
that both cards are kings?
2. Two sisters compete in a race with five friends. The racers draw lots to determine their starting positions. What
is the probability that the older sister starts in lane 1 and the younger sister starts in lane 2?
3. 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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4. A small pouch contains three blue erasers, four yellow erasers, and two red erasers. If two erasers are randomly
selected without replacement, what is the probability that they will be:
a. Two yellow erasers?
c. Two different colored erasers?
b. No yellow erasers?
d. A blue eraser followed by a red eraser?
5.
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6. Hector’s friends have ordered a pizza which is randomly topped with three of the choices: pepperoni, mushrooms,
peppers, ham, bacon, and onions. Hector enjoys all of the toppings, except pepperoni and onions. What is the
likelihood that the pizza will have:
a. No toppings that Hector dislikes?
c. At least one topping that Hector dislikes?
d. Exactly one topping that Hector dislikes?
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7. Four people line up at a sandwich shop. What is the probability that they will line up in descending order of age?
8. A bag contains 26 equal size marbles, each labeled with a different letter of the alphabet. If three marbles are
drawn at random, what is the probability of selecting an X and a Y?
9. A paper bag contains lollipops of the following flavors: 6 strawberry, 5 lemon, and 1 cherry. Katie selects two
lollipops at random from the bag. Find the probability that Katie selected:
a. 2 strawberry flavored lollipops
b. 1 strawberry flavored and one lemon flavored lollipops.
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10. A cookie jar contains three chocolate chip cookies and six peanut butter cookies, all of the same size. Three
cookies are chosen at random from the jar, without replacement. What is the probability that at least two peanut
butter cookies are chosen?
11. Two teams of two people each must be formed from a group of two men and two women. What is the probability
that the two men will be on the same team?
12. A pencil holder contains five red pencils and three green pencils. Without looking, you randomly select two
pencils. What is the probability that you will
a. Select two red pencils?
b. Not select two green pencils?
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13. A mother, father and their three children randomly stand in a row for a family picture. What is the probability
that the parents will be standing next to each other?
The U.S. Senate consists of two senators from each of the 50 states. Five senators are to be selected at random to
form a committee. What is the probability that no two members of the committee are from the same state? We
will solve this problem by first selecting a state, then one of the two senators from that state.
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