11.4 Tree Diagrams 697 counting principle to determine the number of outcomes in the sample space if the cards are dealt a) with replacement. 11,664 b) without replacement. 11,556 7. Euchre Deck Euchre is a card game played with a deck that contains 24 cards. If two cards are drawn from a euchre deck, determine the number of possible outcomes if the cards are drawn a) with replacement. 576 b) without replacement. 552 8. Pinochle Deck Pinochle is a card game played with a deck that contains 48 cards. If two cards are drawn from a pinochle deck, determine the number of possible outcomes if the cards are drawn a) with replacement. 2304 b) without replacement. 2256 Problem Solving In Exercises 9–26, use the fundamental counting principle to determine the answer to part (a). Assume that each event is equally likely to occur. 9. Coin Toss Two coins are tossed. a) Determine the number of sample points in the sample space. 4 b) Construct a tree diagram and list the sample space. * Determine the probability that c) two tails are tossed. 1 4 d) exactly one tail is tossed. 1 2 e) no tails are tossed. 1 4 f) at least one tail is tossed. 3 4 10. Zebras Eliza is a zebra in the Madison Zoo. The zoo would like Eliza to have two offspring. a) Determine the number of sample points in the sample space of the possible arrangements of male offspring (M) and female offspring (F). 4 b) Construct a tree diagram and list the sample space. * Determine the probability that Eliza has c) two male offspring. 1 4 d) a male offspring and then a female offspring. 1 4 e) no male offspring. 1 4 f) at least one male offspring. 3 4 11. Cards A box contains three cards. On one card there is a sun, on another card there is a question mark, and on the third card there is an apple. Use S for sun, Q for question mark, and A for apple. Two cards are to be randomly selected with replacement. a) Determine the number of sample points in the sample space. 9 b) Construct a tree diagram and list the sample space. * Determine the probability that c) two cards containing apples are selected. 1 9 d) No cards containing an apple are selected. 4 9 e) at least one card that contains an apple is selected. 5 9 12. Cards Repeat Exercise 11 but assume that the cards are drawn without replacement. * 13. Marble Selection A hat contains four marbles: 1 yellow, 1 red, 1 blue, and 1 green. Two marbles are to be randomly selected without replacement from the hat. a) Determine the number of sample points in the sample space. 12 b) Construct a tree diagram and list the sample space. * Determine the probability of selecting c) exactly 1 red marble. 1 2 d) at least 1 marble that is not red. 1 e) no green marbles. 1 2 14. Desk Drawer Ryan’s desk drawer contains 4 pens each with a different color ink–black, green, purple, and red. Ryan randomly selects two pens without replacement from the drawer. a) Determine the number of sample points in the sample space. 12 b) Construct a tree diagram and list the sample space. * *See Instructor Answer Appendix Shllabadibum Bubidibam/ Shutterstock
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