Question

2- (10 pts. Choose the correct answer (Write down the correct answer letter AND value at your answer booklet IF YOU CHOOSE "None of the above", WRITE DOWN THE CORRECT ANSWER: a. I have a bag with 3 coins in it. One of them is a fair coin, but the others are biased coins. When flipped, the three coins come up heads with probability 0.5, 0.6, 0.1, respectively. Suppose you pick one of these three coins uniformly at random and flip it three times (with replacement. The probability of getting HHT (Head then Head Then Tail) is (A) 302/3000 (B) 309/1503 (C) 107/3000 (D) 403/5000(E) none of the above 2p b. If the continuous random variable X is uniformly distributed with a mean of 45 and a variance of 75. The probability that X lies between 40 and 50 is: (E) none of the above 2pt. A 12(B) 1/4 (C) 1/3 There are 3 arrangements of the word DAD, namely DAD, ADD, and DDA. How many arrangements are there of the word PROBABILITY? (B) 1562008 (C) 9979200 (D) 3256617(E) none of the above Suppose now that events A, B and C are mutually independent and P(A)-03, P(I) PIC-.5. Then P(A nBnC) equals: (A) 0.075 (D) 2/3 c. (A) 1457861 d. .4 and (B) 0.06 (C) 0.15 (D) 0.02 (E) none of the above A test is graded on the scale 0 to I, with 0.55 needed to pass. Student scores are modelled by the shown PDF The probability that a student selected at random passes is: (A) 0.25 (B) 0.75 (C0.5 (D) 0.13 (E) None of the above e. /(r)- 4-4x for 1/25 1 otherwis

Answer 1

This probability can also compute by R using command punif(50,30,60)-punif(40,30,60).It gives same answer as I have computed. You can cross check.