Chapter 72 webassign udentAssignment MISS A No Access a When

Chapter 72 webassign udent/Assignment. MISS A No. Access a When the Emperor wr X TD Bank lobs lob de Brother, rm oing-L O IGet oesce lobs Mso G nwent 1 117 2040 An experiment consists of recording the sex composition, in order of their births, of a four-child family in which the children were born at different times. Assuming that a bey is equally likely as a girl to be born into a family, what is the probability that a four-child family chosen at random will have the following? (a) Three girls and a boy in the family 16 b) A youngest child in the family who is a girl (c) An oldest child and a youngest child in the family who are both girts Need Help? L Read Talatea Submit Answer save Progress Practice Another Version Home My Assignments

Solution

Since a boy is equally likely to be born, as a girl, in the family, therefore, the probability of a boy being born in the family is P(B) = ½. Now, since the order does not matter, the probabilty of there being 3 boys ( and 1 girl) in the family is C(4,3)(1/2)4 = [4!/3!(4-1)!]*(1/2)4 = 4/16 = ¼. We know that the probability of a boy being born in the family is P(B) = ½. Similarly, the probability of a girl being born in the family is P(G) = ½ . Then, the probability of the youngest child is a girl is P(G) = ½. Since the oldest and the youngest children being girls does not mean that the 2nd and the 3rd children cannot be girls, the probability of the oldest and the youngest children being girls is (1/2)*( ½) = ¼.