Question

(b) IULUI SAPT Two dice are rolled. Find the probabilities of the following events. 13. The first die is 3 or the sum is 8. 14. The second die is 5 or the sum is 10. One card is drawn from an ordinary deck of 52 cards. Find the probabilities of drawing the following cards. 15. (a) A 9 or 10 (b) A red card or a 3 (c) A 9 or a black 10 (d) A heart or a black card (e) A face card or a diamond 16. (a) Less than a 4 (count aces as ones) (b) A diamond or a 7 (c) A black card or an ace (d) A heart or a jack (e) A red card or a face card (e) Ifdice A and Care rolled, find the proud (d) Which die is better? Explain. 24. In the "Ask Marilyn" column of Parade wrote about the following game: You and I your die is higher than mine, you win. Oth reader thought that the probability that each Is this correct? If not, what is the probabili wins? Sourer: Parade magazine. 25. Define what is meant by odds. 26. On page 134 of Roger Staubach's autobiog Lifetime to Go, Staubach makes the followin ing his experience in Vietnam: "Odds against a direct hit are very low but danger, you don't worry too much about th Is this wording consistent with our definiti against? How could it have been said so correct? Source: First Down, Lifetime to Kristina Karganova invites 13 relatives to a party: her mother, 2 aunts, 3 uncles, 2 brothers, 1 male cousin, and 4 female cousins. If the chances of any one guest arriving first are equally likely find the probabilities that the first guest to arrive is as follows. 17. (a) A brother or an uncle (b) A brother or a cousin (c) A brother or her mother 18. (a) An uncle or a cousin (b) A male or a cousin (c) A female or a cousin A single fair die is rolled. Find the odds in results in Exercises 27-30. 27.3 28. 4. 5, or 6 29. 2. 3. 4. or 5 30. Some num 31. A marble is drawn from a box containin and 11 blue marbles. Find the odds in f following. (a) A yellow marble (b) A blue (c) A white marble (d) Nord 32. Two dice are rolled. Find the odds of (Refer to Figure 18.) (a) A sum of 3 (b) A sur (c) A sum less than 5 (d) Nota 33. What is a probability distribution? 34. What conditions must hold for a probab acceptable? The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement. Find the probabilities in Exercises 19 and 20. 19. (a) The sum of the numbers is 9. (b) The sum of the numbers is 5 or less. (c) The first number is 2 or the sum is 6. 20. (a) Both numbers are even (b) One of the numbers is even or greater than 3. (c) The sum is 5 or the second number is 2. Use Venn diagrams to work Exercises 21 and 22. 21. Suppose P(E)-0.26. PF) = 0.41. and PE F) - 0.16. Find the following (a) P(E U F) (b) PE F) (e) P( E F ) (d) P(E UP) 22. Let P(Z) - 0.42. P(Y) = 0.35, and P(Z UY) - 0.59. Find cach probability (a) PIZ' Y') (b) P(Z UT) (e) P(Z UY) (d) P(Z Y") 23. Three unusual dice, A, B and C, are constructed such that die A has the numbers 3.3.4.4.8.8; die B has the numbers 1.1.5.5. 9,9; and dic C has the numbers 2.2, 6, 6, 7.7. (a) If dice A and B are rolled, find the probability that beats 4that is, the number that appears on die B is greater than the number that appears on die A. An experiment is conducted for which S = ($1. 83, 5, 5, 5s}. Which of the pro in Exercises 35-40 are possible for this assignment is not possible, tell why. 35. Outcomes Probabilities 0.09 0.32 0. 36. Outcomes Probabilities 5 5 0.92 S 0.03 37. Outcomes Probabilities 1/3 1/4 38. Outcomes Probabilities 1/5 1/ 3 1

Answer 1

from an ordinary one deck cand ii drawn of 52. less than a 4 ( Count ases as ones). 4P71) + 4p(2)+ 4 PC3) pl 1) = 1 p (2) = 1 P13) = 1 52 - 3 13 52 26 A diamond or a 7 p= pediamond) + P(7) LA block card or an po pc black card) + are place) - 13+ 2 = 15 ① P = A heart or a jack pl heart ) t pe jack) 52 ce p. = a red card of a face cand pered cand) + p (face cand) 26+ 12 = 38 (9) 52577

PAGE NO.: (22) D( 21)-1-0.42= piz)=0.42 ply) = 0.35 .58 Ply) = 1-0.35 65 PIZUY) -0.59 (a) pralny') Przux)] (de-morgan low) 10:59 6.41 (b) P 12'uv' = P(2') + Ply') - P(ziny) - 58+.65- 0.41 58 +.24 .82 O PlZlur) = P(21)+pl-Pliny) 58 35- 1- P(z) + Pizny) = -0.42 +0.18 7 Pizny) = P12vy) + P12) + Ply = -0.59 + 0.42 +0:35 2 -0.17 +0.35 = 0.18 I- 0.2 4 = 0.76 plz nr) - P12) PlznK) = 0.42 - at 0:18 = 0.24