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# 11.5 Probability with Fundamental Counting Principles, Permutation and Combination

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### 11.5 Probability with Fundamental Counting Principles, Permutation and Combination

1. 1. 11.5 Probability with the Fundamental Counting Principles, Permutations and Combinations<br />
2. 2. Three Kinds of Probability<br />Theoretical Probability<br />Empirical Probability<br />Subjective Probability<br />
3. 3. Probability with FCP (Problem # 1)<br />A restaurant offers 3 appetizers (salad, soup, breadsticks), 4 main courses (chicken, beef, fish, pork) and 2 desserts (cake and ice cream). What is the probability of getting a soup, chicken and ice cream for a meal?<br />1/24<br />
4. 4. Probability with FCP (Problem # 2)<br />Mr. P has 4 ties (Cartoon character, Navy Blue, Black, Striped), 4 shirts (white, blue, black and gray) and 4 pairs of pants (black, brown, beige and gray). What is the probability that he will wear a black tie, black shirt and black pants?<br />1/64<br />
5. 5. Probability of a Permutation<br /> Number of ways the permutation can occur Total number of permutations<br />
6. 6. Probability with Permutations (Problem # 3)<br />Jay-Z, Jeremih, R. Kelly and T.I. were invited to the 50th celebration at Seton. They arrived randomly and each person arrived at different time.<br />In how many ways can they arrive?<br />In how many ways can Jay-Z arrive first and T.I. last?<br />What is the probability that Jay-Z arrive first and T.I. last? <br />
7. 7. Answer:<br />Total Permutation: 4! = 24<br />No. of permutations for Jay Z to arrive first and T.I. last = 1 x 2 x 1 x 1 = 2<br />c. Probability = 2/24 = 1/12<br />
8. 8. Probability with Permutations (Problem # 4)<br />Suppose that you want to arrange the 4 Twilight books. <br />What is the probability that Breaking Dawn (the last book in the series) is placed at the end? <br />What is the probability that Twilight (the first book in the series) is placed first and New moon (the second in the series) placed second?<br />6/24 or ¼<br />2/24 or 1/12<br />
9. 9. Probability with Permutations (Problem # 5)<br />Miley Cyrus, Taylor Swift, DemiLovato, Lady GaGa and Kelly Clarkson agree to hold a concert. What is the probability that Lady GaGa will perform first and Kelly Clarkson last?<br />6/120 = 1/20<br />
10. 10. Probability of a combination<br /> Number of ways the combinations can occur Total number of combinations<br />
11. 11. Probability with Combinations (Problem # 6)<br />A poker hand consists of five cards.<br />a. Find the total number of 5-card poker hands.<br />b. A heart flush is a 5-card hand that consists of all hearts. Find the number of possible heart flush.<br />c. Find the probability of being dealt a heart flush?<br />A. Total Combination:<br /> 2,598,960<br />Possible Combination for heart flush: 1287<br />Probability: 1287/2,598,960<br />
12. 12. Probability with Combinations (Problem # 7)<br />To play the Powerball, a player needs to select five numbers from 1-59 and a powerball number from 1-39. <br />a. What is the chance of winning the top prize if you buy one ticket? <br />b. What is the chance of winning the top prize if the cost for one ticket is \$1 and you spent \$100?<br />A. 1/195,249,054<br />B. 50/97,624,527<br />
13. 13. Probability with Combinations (Problem # 8)<br />To play the DC Lotto Hot Sizzler, a player must select 5 numbers from 1-39 and 1 number from 1-19. What is the probability of winning the top prize if you only purchased one ticket? 100 tickets? 1000 tickets? 10,000 tickets?<br />One ticket: 1/10,939,383<br />1000 tickets: <br />1000/10,939,383<br />10,000 tickets:<br />10,000/10,939,383<br />
14. 14. Probability with Combinations (Problem # 9)<br />A group consists of 6 men and 10 women. Four members are selected at random to attend a conference. Find the probability that the selected group consists of <br />A. All men<br />B. All women<br />C. 2 men and 2 women<br />A. 3/364<br />B. 3/26<br />C. 135/364<br />
15. 15. Probability with Combinations (Problem # 10)<br />A box contains 20 IPods, where 5 of them are defective. If 5 are selected at a random, find the probability that<br />A. All are defective<br />B. None are defective<br />A. 1/15504<br />B. 1001/5168<br />
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