I need help with these counting/probability questions. ace F4 FS F6 F7 The follo
ID: 3363811 • Letter: I
Question
I need help with these counting/probability questions.
ace F4 FS F6 F7 The following questions are not related. (a) (15 pts) The 6 hat experiment is performed with three married couples. Find the probability of A, derangement (nobody gets their own hat), of B, the event that each woman got her own husband's hat, and of C, the event that each man got his own wife's hat. endent? Are B and C independent? Are they pairwise independent? two from each state - and 21 of them are women. In fact in three states (Cal., N. Hamp., Wash.) both of the senators are women and in ifteen other to form a waiting line to get a Explain. (b) (10 pts) The US senate has 100 senators- states, ONE of the two senators is a woman. i. At lunch time all 100 senators were lined up "at random" size. seat for lunch. Carefully describe the sample space for this experiment and give its ii. What is the probability that the first and last senators in the line are women? ii What is the probability that the two senators from each state are adjacent in the line? Explain. Explain your answer.Explanation / Answer
b)
i) Here the sample space is the US senate of size 100.
ii) Two women for the first and last position in the queue can be selected in 21C2 ways. And these two women can be arranged among themseleves in 2! ways.
Remaining 98 senators can be arranged in 98! ways.
Hence total possible ways arrangement such that first and last senators in the line are women = 21C2 * 2! * 98!
Total possible arrangements are = 100!
Required probability = (21C2 * 2! * 98!)/100! = 21C2*2/(99*100) = 0.0424
iii)
If 2 senators from each state has adjacent to be other, there are 50!*2! possible ways of doing this.
Required probability = 50!*2!/100!