Question 6 Not yet answered Marked out of 1.00 V Flag question Rules of probability learned in module 2, lecture supplements and office hours of module week 6 Customers leaving a subway station can exit through any one of three gates, Assuming that any particular customer is equally likely to select any one of the three gates, find the probability that in a sample of four customers all four select the same gate. Select one: C) a. 0.037 0 b. 0.71 o c. 0.211 0 d. 0.234 Question 7 Not yet Let the random variable X represent the number of children in a family of a certain community. It is known that 15 percent of the families have no children, 20 answered percent have 1, 35 percent have 2, and 30 percent have 3; and suppose, further, that in Marked out of 1.00 each family, each child is equally likely (independently) to be recorded as a boy or a girl. If a family is Flag chosen at random from this community, then B, the number of recorded boys, and G, the number of recorded girls, in this family will have the joint probability mass function shown question below G=0 G=1 G=2 G=3 B=0 0.15 0.1 0.0875 0.0375 B=1 0.1 0.175 0.1125 B=2 0.0875 0.1125 10 3=3 0.0375 0 10 What is the expected number of girls, E(G) equal to? Select one or more: O a. E(G) = _ XE(GIX = x)P(X = x) O b. 0.9 O c. 0.5 O d. 0.1075Question 8 Not yet answered Marked out of 1.00 '7 Flag question A multinomial coefficient appears when we try to compute which of the following? Select one: Q a. The number of people visiting UCLA every year 0 b. The number of ways to multiply probabilities 0 cl The number of ways to allocate n number of people to a group of k. 0 d The number of ways to allocate n number of people to k groups of different or equal sizes. 0 e, The number of ways to select a group of 3 people where one is president and the other secretary and the other maid