probability success failure sample space random variable probability distribution

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2 probability success failure sample space random variable probability distribution

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4 Probability with Combinations Roman has a collection of 26 books 16 are fiction and 10 are nonfiction. He randomly chooses 8 books to take with him on vacation. What is the probability that he chooses 4 fiction and 4 nonfiction? Step 1 Determine how many 8-book selections meet the conditions. 16C 4 4 fiction books chosen from 16 fiction books 10C 4 4 nonfiction books chosen from 10 nonfiction books

5 Probability with Combinations Use the Fundamental Counting Principle to find s, the number of successes. Step 2 Find the total number, s + f, of possible 8-book selections. Step 3 Determine the probability. P(4 fiction, 4 nonfiction)

6 Probability with Combinations Probability formula Substitute. Use a calculator. Answer: The probability is about or 24.5%.

7 Ensley has a collection of 15 CDs 5 are jazz and 10 are blues. She randomly chooses 7 CDs to take with her on vacation. What is the probability that she chooses 2 jazz and 5 blues? A. 0.7% B. 18.1% C. 39.2% D. 46.7% A B A. A B. B C. C 0% D. D 0% 0% 0% C D

8 Probability with Permutations For next semester, Alisa has signed up for English, precalculus, Spanish, geography, and chemistry classes. If classes are assigned randomly and each class is equally likely to be at any time of day, what is the probability that Alisa's first two classes in the morning will be precalculus and chemistry, in either order. Step 1 Determine how many class arrangements meet the conditions. 2P 2 3P 3 Choose the first 2 classes. Choose the other 3 classes.

9 Probability with Permutations Use the Fundamental Counting Principle to find the number of successes. Step 2 Step 3 2P 2 3 P 3 = 2! 3! or 12 Find the total number, s + f, of possible 5-class selections. 5P 5 = 5! or 120 s + f = 120 Determine the probability. P(precalculus, chemistry, followed by other classes)

10 Probability with Permutations Probability formula Substitute. Use a calculator. Answer: The probability of Alisa scheduling precalculus and chemistry as her first two classes is 0.1 or 10%.

11 Travis and Cody are competing against four other athletes in the javelin throw. If all of the athletes randomly draw for the order in which they will throw, what is the probability that Travis and Cody will throw first or second in any order? A. 6.7% B. 7.4% C. 8.3% A. A B. B C. C 0% D. D 0% 0% 0% A B C D D. 8.5%

12 Probability with Combinations and Permutations Suppose Alice draws 4 cards without replacement from a standard 52-card deck. What is the probability that those 4 cards contain 2 of one suit and 2 of another? Step 1 4P 2 13C 2 13C 2 Determine the number of successes. 2 suits chosen from 4 if order matters 2 cards of one color chosen from a group of 13 2 cards of one color chosen from a group of 13

13 Probability with Combinations and Permutations Use permutations and combinations, along with the Fundamental Counting Principle, to find s. 4P 2 13 C 2 13 C 2 = or 73,008 Step 2 Determine the number of possibilities, s + f. 52C 4 = 270,725 ways to choose 4 cards from a deck of 52.

14 Step 3 Probability with Combinations and Permutations Find the probability. Probability of success s = 73,008 and s + f = 270, Use a calculator. Answer: The probability that Alice draws 4 cards that contain 2 of one suit and 2 of another is about or 27%.

15 Suppose Alice draws 6 cards without replacement from a standard 52-card deck. What is the probability that those 6 cards contain 3 of one suit and 3 of another? A. 4.8% B. 5.6% C. 6.1% D. 6.8% A B A. A B. B C. C 0% D. D 0% 0% 0% C D

16 Probability Distribution A. A bag of 10 marbles contains 3 blue, 1 red, 2 yellow, and 4 green marbles. Create a relativefrequency graph of the probability distribution. Answer:

17 Probability Distribution B. A bag of 10 marbles contains 3 blue, 1 red, 2 yellow, and 4 green marbles. Use the graph to determine which outcome is most likely. What is its probability? Answer: The most likely outcome is green, and its probability is.

18 Probability Distribution C. A bag of 10 marbles contains 3 blue, 1 red, 2 yellow, and 4 green marbles. What is the probability of drawing a red or blue marble? Answer: The probability of drawing a red or blue marble is.

19 A. A bag of 10 marbles contains 3 purple, 4 grey, 2 clear, and 1 black marble. Create a relativefrequency graph of the probability distribution. A. B. C. D. A. A B. B C. C 0% D. D 0% 0% 0% A B C D

20 B. A bag of 10 marbles contains 3 purple, 4 grey, 2 clear, and 1 black marble. Use the graph to determine which outcome is most likely. What is its probability? A. grey; B. purple; C. grey; D. clear; A 0% 0% 0% 0% B C D A. A B. B C. C D. D

21 C. A bag of 10 marbles contains 3 purple, 4 grey, 2 clear, and 1 black marble. What is the probability of drawing a grey or clear marble? A. B. C. D. A 0% 0% 0% 0% B C D A. A B. B C. C D. D

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