Answer:
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
