1. Review Sheet 8, 11-19, 25 OBJ: Review for Probability Quest 2

2. 1. Two cards are chosen at random from a deck of 52 cards without replacement. What is the probability of getting two kings? 4/663 1/221 1/69 None of the above 4/52 · 3/51 = 12/2652 = 1/221 Two cards are chosen at random from a deck of 52 cards without replacement. What is the probability that the first card is a jack and the second card is a ten? 3/676 1/169 4/663 None of the above 4/52 · 4/51 = 16/2652 = 4/663 On a math test, 5 out of 20 students got an A. If three students are chosen at random without replacement, what is the probability that all three got an A on the test? 1/114 25/1368 3/400 None of the above 5/20 · 4/19 · 3/18 =60/6840 = 1/114 Three cards are chosen at random from a deck of 52 cards without replacement. What is the probability of getting an ace, a king and a queen in order? 1/2197 8/5525 8/16575 None of the above 4/52 · 4/51 · 4/50 = 64/132600 = 8/16575 A school survey found that 7 out of 30 students walk to school. If four students are selected at random without replacement, what is the probability that all four walk to school? 343/93960 1/783 7/6750 None of the above 7/30 · 6/29 · 5/28 · 4/27 =840/657720 = 1/783

3. 13. One card is drawn from a regular deck. What is the probability that it is a queen if it is known to be a face card? P(Q/F) = n(Q and F)/n(F) ( = P(Q and F)/P(F)) = 4 12 = 1 3

4. In New York State, 48% of all teenagers own a skate board, and 39% of all teenagers have roller blades and a skate board. What is the probability that a teenager who has roller blades also has a skate board? 87% 81% 123% None of the above P( SB/ RB) = P(SB  RB)/P(RB) =.39 ÷.48 =.8125 At a middle school, 18% of all students play football and basketball, and 32% of all students play football. What is the probability that a student who plays football also plays basketball? 56% 178% 50% None of the above P( BB/ FB) = P(BB  F B)/P(FB) =.18 ÷.32 =.5625 In the United States, 56% of all children get an allowance, and 41%of all children get an allowance and do household chores. What is the probability that a child does household chores given that he/she gets an allowance? 137% 97% 73% None of the above P( HC/ AL) = P(HC  AL)/P(AL) =.41 ÷.56 =.7321 In Europe, 88% of all households have a television. 51% of all households have a television and a VCR. What is the probability that a houshold with a television also has a VCR? 173% 58% 42% None of the above P(VCR/ TV) = P(VCR  TV/P(TV) =.51 ÷.88 =.5795 In New England, 84% of the houses have a garage. 65% of the houses have a back yard and a garage. What is the probability that a house has a backyard given that its has a garage? 77% 109% 19% None of the above P(G/ BY) = P(G  BY/P(BY) =.65 ÷.84 =.7738

5. 12) A pair of dice is thrown. Find the probability that the dice match, given that their sum is greater than five. P(dice match/sum >5) = 4 26 = 2 13 (1,5)(1,6) (2,4)(2,5)(2,6) (3,3)(3,4)(3,5)(3,6) (4,2)(4,3)(4,4)(4,5)(4,6) (5,1)(5,2)(5,3)(5,4)(5,5)(5,6) (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

6. 14. A pair of dice is thrown. Given that their sum is > 9, find a. P(sum is 8) 0 b. P(numbers match) 2 = 1 10 5 c. P(sum is 12) 1 10 d. P(sum is even) 4 = 2 10 5 e. P(sum is 9 or 10) 7 10 f. P(numbers match or sum is even) 2 + 4 _ 2 10 10 10 2/5 9 910 9 11 9101112

7. 8)There are 4 navy socks and 6 black socks in your drawer. One dark morning you randomly select 2 socks. What is the probability that you will choose a navy pair? With Replacement 4 4_ 10 2 2_ 5 5 4_ 25 Without Replacement 4 3 10 9 2 1_ 5 3 2_ 15

8. 25. There are 8 girls and 5 boys in my class. If I randomly select 4 students to go to the board, find the following (Use combination notation) a.P(all girls) = 8 C 4 5 C 0 13 C 4 b. P(2 girls and 2 boys) = 8 C 2 5 C 2 13 C 4 c. P(1 girl and 3 boys) = 8 C 1 5 C 3 13 C 4

9. The students that go to the board are to be 2 seniors and 2 juniors, who are to be chosen at random from the 6 seniors and 7 juniors. If half of the seniors and 4 juniors are girls find the probability that only girls go up to the board(Use combination notation) 3 C 2 3 C 0 4 C 2 3 C 0 13 C 4

10. 19a. (2c – 1) 5 1( ) 5 – 5( ) 4 + 10( ) 3 – 10( ) 2 + 5( ) 1 – 1 1(2c) 5 – 5(2c) 4 + 10(2c) 3 – 10(2c) 2 + 5(2c) 1 – 1 32c 5 – 5(16c 4 ) + 10(8c 3 ) – 10(4c 2 ) + 5(2c) – 1 32c 5 – 80c 4 + 80c 3 – 40c 2 + 10c – 1

11. 19b. third term of (3x + 2y) 6 1( ) 6 + 6( ) 5 ( ) 1 + 15( ) 4 ( ) 2 15(3x) 4 (2y) 2 15(81x 4 )(4y 2 ) 4860x 4 y 2

12. 16.While pitching for the Toronto Blue Jays, 4 out of every 7 pitches that Juan Guzman threw in the first five innings were strikes. Find the probability that three of his next four pitches will be strikes. n C k p k (1-p) n-k n=4, k=3, p=4/7,1-p=3/7 4 C 3 (4/7) 3 (3/7) 1 = 4 (4 3 /7 3 ) (3/7)= 4 4 3 = 768 7 4 2401 From HW 6 6. What is the probability of getting K #s in N rolls of a die? P = 1/6 1-P = 5/6 9. A quiz has N multiple-choice questions, each with # choices. What is the probability of getting K choices correct? P = 1/# 1-P = 1- 1/#

13. 17. Maria guessed at all 10 true/false questions on her math test. Find: a.P(7 correct) = n C k p k (1-p) n-k n=10, k=7, p=1/2, 1-p=1/2 10 C 7 (1/2) 7 (1/2) 3 = 1201 10 = 2 10 120 = 1024 15 128 b.P(all incorrect) = n C k p k (1-p) n-k n=10, k=0, p=1/2, 1-p=1/2 10 C 0 (1/2) 0 (1/2) 10 = 1 1 10 = 2 10 1__ 1024 c. P(at least 6 correct) = n C k p k (1-p) n-k n=10, k > 6, p=1/2, 1-p=1/2 10 C 6 (1/2) 6 (1/2) 4 + 10 C 7 (1/2) 7 (1/2) 3 + 10 C 8 (1/2) 8 (1/2) 2 + 10 C 9 (1/2) 9 (1/2) 1 + 10 C 10 (1/2) 10 (1/2) 0

14. 15)A dollar bill changer was tested with 100 one-dollar bills, of which 25 were counterfeit and the rest were legal. The changer rejected 30 bills, and 6 of the rejected bills were counterfeit. Construct a table, then find a. Incorporate the facts given above into a conditional chart. RR C C

15. 15)A dollar bill changer was tested with 100 one-dollar bills, of which 25 were counterfeit and the rest were legal. The changer rejected 30 bills, and 6 of the rejected bills were counterfeit. Construct a table, then find a. Incorporate the facts given above into a conditional chart. RR C 6 25 C 30 100

16. 15)A dollar bill changer was tested with 100 one-dollar bills, of which 25 were counterfeit and the rest were legal. The changer rejected 30 bills, and 6 of the rejected bills were counterfeit. Construct a table, then find RR C 61925 C 245175 3070100

17. 15)A dollar bill changer was tested with 100 one-dollar bills, of which 25 were counterfeit and the rest were legal. The changer rejected 30 bills, and 6 of the rejected bills were counterfeit. Construct a table, then find RR C 61925 C 245175 3070100 RR C 6 25 C 30 100

18. 15)A dollar bill changer was tested with 100 one-dollar bills, of which 25 were counterfeit and the rest were legal. The changer rejected 30 bills, and 6 of the rejected bills were counterfeit. Construct a table, then find a.The probability that a bill is legal and it is accepted by the machine. P(C  R)= 51 100 b.The probability that a bill is rejected, given it is legal. P(R/C)= 24 = 8 75 25 c.The probability that a counterfeit bill is not rejected P(R/C) = 19 25 RR C 61925 C 245175 3070100

19. 11)Of 200 students surveyed, 100 said they studied for their math test. 105 said they passed their test, and 80 said they studied and passed their test. a. Incorporate the facts given above into a conditional chart. PP S S

20. 11)Of 200 students surveyed, 100 said they studied for their math test. 105 said they passed their test, and 80 said they studied and passed their test. a. Incorporate the facts given above into a conditional chart. PP S 80100 S 105200

21. 11)Of 200 students surveyed, 100 said they studied for their math test. 105 said they passed their test, and 80 said they studied and passed their test. PP S 8020100 S 2575100 10595200 PP S 80100 S 105200

22. 11)Of 200 students surveyed, 100 said they studied for their math test. 105 said they passed their test, and 80 said they studied and passed their test. PP S 8020100 S 2575100 10595200 a)P(pass) 105 200 21 40

23. 11)Of 200 students surveyed, 100 said they studied for their math test. 105 said they passed their test, and 80 said they studied and passed their test. PP S 8020100 S 2575100 10595200 b) P(pass/studied) P(P/S) 80 100 4 5

24. 11)Of 200 students surveyed, 100 said they studied for their math test. 105 said they passed their test, and 80 said they studied and passed their test. PP S 8020100 S 2575100 10595200 _ _ c) P(P/S) 75 100 3 4

25. 18. The probability that a certain softball player gets a hit is 1/5. (20%) In her next 5 at bats, find b. P( at least 4 hits) n C k p k (1-p) n-k n = 5, k ≥ 4, p =.2, 1–p=.8 5 C 4 (.2) 4 (.8) 1 + 5 C 5 (.2) 5 c. P(at least 1 hit) n C k p k (1-p) n-k n = 5, k ≥ 1, p =.2, 1–p=.8 5 C 1 (.2) 1 (.8) 4 + 5 C 2 (.2) 2 (.8) 3 5 C 3 (.2) 3 (.8) 2 + 5 C 4 (.2) 4 (.8) 1 + 5 C 5 (.2) 5 OR 1 – 5 C 0 (.8) 5 The problem on the quest, n=10!!!

26. From HW 12 Conditional Worksheet 1. In a study of the reading habits of 250 college students it was found that 158 read Time magazine, 139 read Newsweek, and 100 read both Time and Newsweek a. Incorporate the facts given above into a conditional chart. TT N N

27. From HW 12 Conditional Worksheet 1. In a study of the reading habits of 250 college students it was found that 158 read Time magazine, 139 read Newsweek, and 100 read both Time and Newsweek Incorporate the facts given above into a conditional chart. TT N 100139 N 158 250

28. From HW 12 Conditional Worksheet 1. In a study of the reading habits of 250 college students it was found that 158 read Time magazine, 139 read Newsweek, and 100 read both Time and Newsweek TT N 10039139 N 5853111 15892250 TT N 100139 N 158250

29. From HW 12 Conditional Worksheet 1. In a study of the reading habits of 250 college students it was found that 158 read Time magazine, 139 read Newsweek, and 100 read both Time and Newsweek. Find the probability that a student: a.Reads Newsweek P(N) 139 250 b.Reads both Time and Newsweek P(T  N) 100 2 250 5 TT N 10039139 N 58 53111 15892 250

30. From HW 12 Conditional Worksheet 1. In a study of the reading habits of 250 college students it was found that 158 read Time magazine, 139 read Newsweek, and 100 read both Time and Newsweek. Find the probability that a student: c.Reads Newsweek given reads Time P(N  T) 100 50 158 79 d.Read Time given reads Newsweek P(T/N) 100/139 TT N 10039139 N 58 53111 15892 250

31. From HW 12 Conditional Worksheet 4.Out of 1000 students surveyed, 10% reported that they had had a car accident since getting their license, 40% reported driving more than 10,000 miles since getting their license and 6% had driven more than 10,000 miles and had an accident. a. Incorporate the facts given above into a conditional chart. AA M M

32. From HW 12 Conditional Worksheet 4.Out of 1000 students surveyed, 10% reported that they had had a car accident since getting their license, 40% reported driving more than 10,000 miles since getting their license and 6% had driven more than 10,000 miles and had an accident. Incorporate the facts given above into a conditional chart. AA M 60400 M 100 1000

33. From HW 12 Conditional Worksheet 4.Out of 1000 students surveyed, 10% reported that they had had a car accident since getting their license, 40% reported driving more than 10,000 miles since getting their license and 6% had driven more than 10,000 miles and had an accident. Incorporate the facts given above into a conditional chart. AA M 60340400 M 40560600 100900 1000

34. From HW 12 Conditional Worksheet 4.Out of 1000 students surveyed, 10% reported that they had had a car accident since getting their license, 40% reported driving more than 10,000 miles since getting their license and 6% had driven more than 10,000 miles and had an accident AA M 60340400 M 40560600 100900 1000 AA M 60400 M 100 1000

35. From HW 12 Conditional Worksheet 4.Out of 1000 students surveyed, 10% reported that they had had a car accident since getting their license, 40% reported driving more than 10,000 miles since getting their license and 6% had driven more than 10,000 miles and had an accident. Find the probability that a student a.Had driven more than 10000 miles without having an accident. P(M  A) 340 17 1000 50 b. Had driven no more than 10000 miles and did not have an __ accident. P(M  A) 560 14 1000 25 AA M 60340400 M 40560600 100900 1000

36. From HW 12 Conditional Worksheet 4.Out of 1000 students surveyed, 10% reported that they had had a car accident since getting their license, 40% reported driving more than 10,000 miles since getting their license and 6% had driven more than 10,000 miles and had an accident. Find the probability that a student c.Who drove no more than 10,000 miles had an accident. P(M/A) 40 1 600 15 d. Who did not have an accident drove more than 10,000 miles. P(A/M) 340/900=17/45 AA M 60340400 M 40560600 100900 1000