Question

A couple wants to have 2 boys and 2 girls. They will continuous to have children until they have reached the goal. Assuming that the probability that they have 54% chance to have a boy and 46% chance to have a girl in every pregnancy. No twin or more are possible. Assuming that their goal is possible and has been fulfilled today! a. What is the probability that they have exactly two boys? b. What is the probability that they have exactly two girls? c. What is the probability that they have more than 4 children? d. What is the probability that they have in between 3 and 5 boys? e. What is the expected value of the number of children they have?

Answer 1

Answer Fren theiven infomna tion, have we 2 boys PLEeartly 2 bys0.5 (o.46+ 054)3 . 44)3 +Co.54) (0.44 a.s4) 0.46)+0. 46 +043 0.54 .41 Lo.46] 0.2916 x0.226 x1/-0.46) 0.06170256 0.54 0.114-264 0.1143 Exaetygils LEacty 2gls46 x6.s 4), (o.46)o.s4 Co.46 .54 o. 460.54)40-54 4p.54) X (0.542 x0.46) L -on54 0.2916 x0.2116 x 11-0.54 o.46 0.061 70256 17 a. 1341

move then 4 childrean :- LE-adt more then 4 child-rean [.- theve is ony less then 4 is vet possible ,se opton dor medinga they hae 4 chi ldren 1.e one -0.54 x O.54 x0.46 X0.46 o.0617 0.9383 2. + PIs bysgs Co. 54)A0.4e.54)4 x.46),6.s4) K0.46) Lo.0610 children 2 boys 54 4-6 Expecled value ok the ro oehiláven they haue knouo that Expecte value ExPCa) 2x Co.54) 2x (o.46) the Expected value-2