Question
Please explain each step
Part II: For maximum credit, show all necessary work and clearly indicate your answer Each numbered problem is worth 25 points. 4. Andy and three of his friends, Bill, Cindy, and Dora, are going 1 on a trip Only Andy, Cindy and Dora can drive. The "1" position in the diagram is the driver's seat. You can represent a seating 3 4 arrangement by the vector (A.B.C.D), which indicates Andy is driving and where his three friends are sitting a. How many different feasible seating arrangements are possible? (That is, with Andy, Cindy or Dora driving). You do not have to list them, but be sure to show me how you got this answer b. If one of the seating arrangements from Part a is selected at fandom, what is the probability that Andy or Dora is driving? Assume the sample space, S, consists of the arrangements from Part a and that all of those arrangements are equally-likely. Round your answer to two decimal places 2. 17 C. If one of the seating arrangements from Part a is selected at random, what is the probability that Bill and Cindy are both in back? (That is, in Seats 3 and 4). Use the same assumptions as in Part b. /2
Explanation / Answer
a) Number of options available for Position 1 = 3
Number of options remaining for position 2 = 3
Number of options remaining for position 3 = 2
Number of options remaining for position 4 = 1
So, Number of seating arrangements possible = 3x3x2x1 = 18
b) P(Andy or Dora is driving) = Number of arrangements with Andy of Dora Driving/18
= 2x3x2x1/18
= 2/3
c) P(Bill and Cindy are both at back) = Number of cases with Bill and Cindy both at back / 18
Number of cases with Bill and Cindy both at back = Number of options for Billy x Number of Options for Cindy after Billy chosing x Number of Options for Andy X Number of Options for Dora after andy chosing
= 2 x 1 x 2 x 1
= 4
P(Bill and Cindy are both at back) = 4/18
= 2/9