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A couple plan s to have children until they get a girl, but they agree that they will not have more than three children even if all are boys. (Assume boys and girls are equally likely.)
a) Create a probability model for the number of children they might have.
b) Find the expected number of children.
c) Find the expected number of boy s they 'll have.

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Respuesta :

Answer:

b) 1.75       c) 0.875

Step-by-step explanation:

lt is given that a couple plans to have children until they get a girl, but they agree that they will not have more than three children even if all are boys.

a) The possible combination for the number of children  that a couple might have  :

  X             1st girl      1st boy, 2nd girl       1st ,2nd boys,3rd girl    1,2,3rd boys Probability-   0.5                 0.25                        0.125                           0.125

b) Expected number of children   :

   1(0.5) + 2 ( 0.25 ) + 3 ( 0.125)  + 3( 0.125)

   =  1+ 0.75

   = 1.75

c) Expected number of boys :

     0 x 0.5  + 1 x 0.25  + 2 x 0.125 + 3 x 0.125

    =    0.875    

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