Chapter 4 Probability WKS 21) Find P(A’ ∩ B’) , P( A ∩ B), and P(A  B ) for each of the following.P(A’ ∩ B’) P( A ∩ B) P(A  B )P(A) = .6P(B) = .4P(A∩B’) = .3P(A) = .6P(B’)= .4P(B’|A) = .3P(A) = .6P(B) = .3P(A∩B’) = .3P(A) = .6P(B) = .3P(A|B’) = .6Use tree or Venn diagrams to solve problems 2-5. 2) 35% of engineering majors at ISU are women, 15% of engineering majors at ISU have a GPA over 3.4, and 55% of engineering majors at ISU have a GPA under 3.4 and are men. 2a) If you randomly select a woman, what is the probability that her GPA is over 3.4? 2b) If you randomly select a person with GPA under 3.4, whatis the probability it is a woman?3) A three man jury has two members each of whom independently has probability p of making the correct decision and a third member who flips a coin for each decision (majority rules). A one-man jury has probability p of making the correct decision. Which jury has the better probability of making the correct decision?4) 3 chips are placed in a bag. One is red on both sides, the second is blue on both sides, and the third is red on one side and blue on the other. A friend randomly selects 1 chip and places it on the table; it is showing a red side up. What is the probability that the color underneath is red?5) A standard 52 card deck is used to randomly select 2 cards. What is the probability that the second card is an ace?Chapter 4 Probability WKS 26) Five faces of a fair die are painted black, and one face is painted white. The die is rolled six times. Which of the following results is more likely?a. Black side up on five of the rolls; white side up on the other roll b. Black side up on all six rolls c. a and b are equally likely 7) If Tahnee flips a coin 10 times, and records the results(Heads or Tails), which outcome below is more likely tooccur, A or B? Explain your choice.8. A bowl has 100 wrapped hard candies in it. 20 are yellow, 50 are red, and 30 are blue. They are well mixed up in the bowl. Jenny pulls out a handful of 10 candies, counts the number of reds, and tells her teacher. The teacher writes the number of red candies on a list. Then, Jenny puts the candies back into the bowl, and mixes them all up again. Four of Jenny's classmates, Jack, Julie, Jason, and Jerry do the same thing. They each pick ten candies, count the reds, and the teacher writes down the number of reds. Then they put the candies back and mix them up again each time. I think the teacher's list for the number of reds is most likely to be (please select one): a. 8,9,7,10,9 b. 3,7,5,8,5 c. 5,5,5,5,5 d. 2,4,3,4,3 e. 3,0,9,2,8. Explain your reason.9. You are to participate in an exam for which you had no chance to study, and for that reason cannot do but guess for each question (all questions being of the multiple choice type, so the chance of guessing the correct answer for each question is 1/d, d being the number of options (distractors) per question; so in case of a 4-choice question, your guess chance is 0.25). Your instructor offers you the opportunity to choose amongst the following exam formats: I. 6 questions of the 4-choice type; you pass when 5 or more answers are correct; II. 5questions of the 5-choice type; you pass when 4 or more answers are correct; III. 4 questions of the 10-choice type; you pass when 3 or more answers are correct. Rank the three exam formats according to their attractiveness. It should be clear that the format with the highest probability to pass is the most attractive format. Which would you choose and