c) A family is chosen at random from all three-child families. What is the probability that the chosen family has one boy and two girls if the family has a boy among the three children?(4 Marks) d) Suppose a class contains 60% girls and 40% boys. Suppose that 30% of the girls have A student is chosen uniformly at random from long hair,and 20%of the boy shave long hair.the class. Calculate the probability that the chosen student will have long hair. (4 Marks) e) Consider the random variable of a set of outcomes of tomorrow's weather S, where S={rain, snow, clear},and X is defined by X(rain)=3, X(snow)=6,and X(clear)=– 2.7.Suppose further that the probability measure P is such that P(rain) = 0.4, P(snow) = 0.15,and P(clear) = 0.45. Compute that following: i.P(X ={ 3,6}) ii. P(X<5) f) Suppose we have an urn containing100 chips, each colored either black B or white W.Suppose further that we are told there are either 50 or 60 black chips in the urn. The chips are thoroughly mixed, and then two chips are withdrawn without replacement. Make an inference about the true number of black chips in the urn, having observed the data s =(s1,s2), where si is the color of the ith chip drawn.(6 Marks) g) In the table below, the column "Observed" gives the observed frequencies of birth months for the children born in a certain country in the year 2010. The column"Expected" gives how many births could have been expected in each month under the hypothesis that all birth dates are equally likely.