(a) For two events A and B, suppose that P(A) = 0.3, P(B) = 0.5, and P(AUB) = 0.6. Calculate P(ANB). (b) If P(A) = 0.6, P(B) = 0.3, P(An Bc) = 0.4, and BCC, calculate P(AU BUCC).
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- 1. The events A and B are such that P(A) = 1/3, P(A'|B) = ¼/4, and P(AUB) = ½. Find a) P(A'nB). Ans: 1/6 b) P(B). Ans: 2/3Three events, A, B and C are such that A and B are mutually exclusive, 3 P(4)= P(C|4)= and P(BnC)= 20 (i) Find P(AnC). (ii) Given that P(AnC)=P(BnC)=P(AUBUC), compute P(C). (iii) Hence, calculate P(AUB|C).If S = {a, b, c} with P(a) = 6P(b) = 7P(c), find P(a).
- 7. Given P(A) = 1/3 and P(B) = 1/2 and P(A U B) = 2/3 . . . (d) Find P(BIA) (e) Are events A & B Independent? (f) Are events A & B Mutually exclusive?You are allowed to take a certain test three times, and your final score will be the maximum of the test scores. Your score in test k, where k = 1, 2, 3, takes one of the values from k to 10 with equal probability 1/(11 − k), independently of the scores in other tests. What is the PMF of the final score?12y 3p A) For the joint probability p(A.B)-5p 13p P(B/A), if y is three times larger than p. 4y. Find P(A). P(B). P(A/B), and 7pl
- A student goes to the library. Let events B= the student checks out a book and D= the student check out a DVD. Suppose that P(B)=0.54 P(D)=0.45 and P(D|B)=0.50 Round each answer to four decimal places. (a) Find P(B′)Enter the exact answer.P(B′)= (b) Find P(D AND B)Enter the exact answer.P(D AND B)= (c) Find P(B|D).Round your answer to three decimal places.P(B|D)= (d) Find P(D AND B′)Enter the exact answer.P(D AND B′)= (e) Find P(D∣B)Enter the exact answer.P(D∣B′)The complement of an event is all possible outcomes not in the event. For example: If A = at least 3 girls are born to a family with 6 kids. Then A' = A compliment is what happens if there are not at least 3 girls = less than 3 girls born to the family. A useful formula: P(A) + P(A' ) = 1 or P(A') = 1 - P(A). If P(A) = 0.194, what is P(A')?We throw a symmetrical dice twice. Let X denote the number of throws in which an odd number of dice fell, and let Y denote the remainder of the product of the dice's rolls divided by 3.Check whether the variables X and Y are (a) independent (b) uncorrelated
- A golf club manufacturer claims that golfers can lower their scores by using the manufacturer's newly designed golf clubs. Eight golfers are randomly selected and each is asked to give his or her most recent score. After using the new clubs for one month, the golfers are asked again to give their most recent score. The scores for each golfer are given in the table below. Is there enough evidence to support the manufacturer's claim? Let d=(golf score after using the newly designed golf clubs)−(golf score before using the newly designed golf clubs)d=(golf score after using the newly designed golf clubs)−(golf score before using the newly designed golf clubs). Use a significance level of α=0.05 for the test. Assume that the scores are normally distributed for the population of golfers both before and after using the newly designed clubs. Golfer 1 2 3 4 5 6 7 8 Score (old design) 93 86 84 96 89 81 92 94 Score (new design) 91 90 80 92 91 77 89 87 Step 1 of 5:State the null and…For any event A, P (A U A) = 1 True or false, I.Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?