A couple plans to have children until they get a girl, but they agree they will not have more than three children, even if all are boys. Assume that the probability of having a girl is 47.00 %. a) Create a probability model for the number of children they'll have. b) Find the expected number of children. c) Find the expected number of boys they'll have. a) X P (Xequals x) 1 nothing 2 nothing 3 nothing (Round to four decimal places as needed.) b) E (X) equals nothing (Round to four decimal places as needed.) c) E (number of boys) equals nothing

a) Let X be number of children

X=1,2,3

P (X=1) = 0.47

P (X=2) = 0.2491

P (X=3) = 0.942923

b) 3.7970

c) 1.6232

Step-by-step explanation:

The complete question is:

A couple plans to have children until they get a girl, but they agree they will not have more than three children, even if all are boys. Assume that the probability of having a girl is 47.00 %.

a) Create a probability model for the number of children they'll have.

X=1,2,3

P (X=1) = ?

P (X=2) = ?

P (X=30=?

(Round to four decimal places as needed

b) Find the expected number of children.

E (X) = ?

c) Find the expected number of boys they'll have.

Expected number of boys=?

Solution:

Probability of a girl = 0.47

Probability of a boy = 0.53

a) P (X=1) = 0.47

P (X=2) = 0.47 * 0.53 = 0.2491

P (X=3) = 0.47 * 0.53 * 0.53 + 0.53 * 0.53 * 0.53

= 0.942923

b) E (number of children) = 1 * P (X=1) + 2 * P (X=2) + 3 * (PX=3)

= 3.796969

c) Y: number of boys

P (Y=1) = 0.53*0.47 = 0.2491

P (Y=2) = 0.53*0.53*0.47=0.46375

P (Y=3) = 0.53 * 0.53 * 0.53 = 0.148875

E (Y) = P (Y=1) * 1 + P (Y=2) * 2 + P (Y=3) * 3

= 0.148875*3 + 0.46375*2+0.2491 * 1

= 1.6232