9/24/2017 #19/Points possible: 1. Total attempts: 1 MyOponMath Assessment A roya

Question

9/24/2017 #19/Points possible: 1. Total attempts: 1 MyOponMath Assessment A royal family has children until it has a boy or until it has three children, whichever comes first. Assum that each child is a boy with probability 1/2. Let X denote the number of boys in this royal family number of girls, and Z the number of children. E(X) E(Z) = Use the fact that Z = X + Y (and therefore E(Z) = E(X) + E(Y)) to find E(Y): #20 Points possible: 1 . Total attempts: 1 -S0.56·This implies Carlie is betting on a game in which each bet has an expected value of -S0.56. This implies Carlie will win $0.56 every time she plays the game. Carlie will lose $0.56 every time she plays the game. O if Carlie plays the game many times, on an average Carlie should expect to lose about S0.56 cach game. 11 nints nossible: 1. Total attempts: 1

Explanation / Answer

19.

The Sequence in which the royal family will have their children is as follows:

B(with probability 1/2)

GB(with probability 1/4)

GGB(with probability 1/8)

and, GGG(with probability 1/8), G stands for girls and B stands for boys

Let X denotes the number of boys in the royal family.

X can take the values 0 (with probability 1/8) and 1 (with probability 1/2+1/4+1/8=7/8)

Therefore, E(X)=0*1/8+1*7/8=7/8

Z denotes the number of children in the royal family.

Z can take the values 1,2,3 with respective probabilities 1/2, 1/4, (1/8+1/8)=1/4

E(Z)=1*1/2+2*1/4+3*1/4=7/4

Y denotes the number of girls.

Therefore, Z=X+Y

E(Y)=E(Z)-E(X)=7/4-7/8=7/8

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