Question

2- 0pts./ Multiple Choices (Write down the correct answer letter AND value at your answer Booklet a Three fair dice are rolled. The probability that the sum of the three ouicomes is lo given that the three dice show different outcomes is: (A) 3/20 (B) 5/20 () 10/216 D) 30/216 (E) none of the above Irx'is a CRV uniformily distributed with a mean o 0 and a variance or 73. the probability that X lies between 30 and 40 is: A) 1/2 (B) 1/4 C)1/3 (D) 2/3 (E) none of the above c You purchase a certain product of lifetime T (in years) that satisfies the following rule: PIt)-e 5) for t20. What is the probability that this device breaks down during the third year? (A) 0.67 (B) 0.549 (C) 0.122 (D) 0.181 (E) none of the above d Suppose now that events A, B and C aré mutually independent and PIA)-0.3, P(B)-0.4 and P(C)-0.5. Then PA n Bequals: (A) 0.075 (B0.0(C)0.15 (D) 0.02 (E) none of the above (C) 0.15 (D) 0.02 (E) none of the above eA test is graded on the scale 0 to 1, with 0.55 needed to pass. Student scores 4r for 0 are modelled by the shown PDF. The probability that a randomly selected student passes is: (A) 0.25 (B) 0.75 (C) 0.5 (D) 0.13 (E) None of the above otherwise

With explanation please.

Answer 1

2)

a)

Number of ways three dice show different outcome = 6*5*4 =120

x1 + x2 +x3 = 10 where xi are all different and 1 <= xi <=6

(1,3,6),(1,4,5),(1,5,4),(1,6,3),

,(2,3,5),(2,5,3),

(3,1,6),(3,2,5),(3,5,2),(3,6,1)

(4,1,5),(4,5,1)

(5,1,4),(5,2,3),(5,3,2),(5,4,1)

(6,1,3),(6,3,1)

total number of ways = 18

hence required probability = 18/120 = 3/20

option A) is correct

Please post one question at a time