HW problems 3-2

1. HW problems 3-2 p. 121 #14. A study of 150 randomly selected American Airlines flights showed that 108 arrived on time (DOT). a) What is the probability of arriving late on an AA flight? b) Is it unusual to arrive late on AA? A: a) P(late on AA) = 42 / 150 = 0.28 b) Arriving late on AA is not unusual! p. 122 # 17. a) Probability of randomly selecting person with b-day on October 18. b) Probability of birthday in October. c) Probability of randomly selecting a person born on a day of the week ending on y. • P(Oct 18) = 1/ 365 • P(October) = 31/365 • P(‘birth on day ending in ‘y’) = 1

2. . 130 # 13-20 • P(not gpA) • P(type Rh-) • P(gp A or ty Rh-) • P(gp A or gp B) • P(not ty Rh+) • P(gpB or ty Rh+) • P(gp AB or Rh+) • P(A or O pr Rh+) =60/100 =14/100 =(40+14–5)/100=0.39 =50/100 disjoint =14/100 see (b) =0.1+0.86–0.08=0.88 =0.85+0.86- (0.39+0.35) = .85+.86-.74 =0.97 (3 not Rh+ or AO) HW problems 3-3 and 3-4 p. 138 #11. a) What is the probability that 2 randomly selected people have b-day on Nov. 27? b) What is the probability that 2 randomly selected people have same b-day? A: a) P(b-day of John and Jack on Nov 27) = 1/365 * 1/365 = 1/133225 = 0.00000751 b) P(same birthday) = 365 different DAYS* 1/365*1/365 = 1/ 365

3. HW problems 3-4 and 3-5 p. 139 #13. Acceptance sampling. If all items in sample without replacement are good, batch accepted. Batch 5000 CDs, 3% defective. Sample 12 at random. a) What is the probability that the batch will be accepted? A: a) P(batch accepted) = 0.97 12 = 0.694 p. 147 # 19-21 Titanic example. P(man|died) = P(man & died)/P(died) P(died |man) = P(man & died )/P(man) P(A |B )=P( A and B) / P(B)

4. At least one = one or more Complement: none! P(at least one girl among 3 children) = 1- P(no girl) =1-1/8 =7/8 =0.875 P(at least one poll within confidence interval) =1- P(no poll good) =1- [ 0.05 5] = 0.9999997 happens always! The conditional probability of the event A given B is denoted by P(A | B)and it is the probability that A occurs knowing thatB has occurred already Conditional probability “At least one” event boy-boy-boy boy-boy-girl boy-girl-boy boy-girl-girl girl-boy-boy girl-boy-girl girl-girl-boy girl-girl-girl • 1 subject is selected randomly, find the probability of a subject being positive, given that she is pregnant. P(pos|pregnant) = 80/85=0.941 or = P(positive and pregnant) P(pregnant) = 80/99 = 0.964 85/99

5. Conditional Probability Titanic • P(man |died) • P(died |men) • P(boy or girl |survived) • P(man or woman| died) P(man|died) = P(man & died)/P(died) =1360/1517=0.897 P(died |man) = P(man & died )/P(man) =1360/1692=0.804 P(boy or girl |survived)=P( {boy or girl} & survived)/P(survived)=57/706=0.079 P(man or woman| died) )=P({man or woman}& died)/P(died)=1464/1517=0.965 NOTE: P(man & died) = 1360 / 2223 = 1360 = 0.897 P(died) 1517 / 2223 1517

6. HW problems 3-6 p. 155 #9. Probability of winning Mass Lotto: 6 numbers from 1,…,49 A: a) P(win) = 1/49C6= 1 / 13,983,816 p. 156 # 22 Board of directors. 12 members on board. • Elect chair, vice-chair, 2nd vice-chair, and secretary. How many different slates? • Ethics subcommittee. 4 members. How many subcommittees possible? • C,VC1,VC2, S: ORDER MATTERS! 12P4= 11,880 • Subcommittee: ORDER DOES NOT MATTER! 12C4= 495