Example B) A second couple is also planning on having three children but they ha

Question

Example B) A second couple is also planning on having three children but they have visited the Genetics and IVF Institute in Fairfax, Virginia (see the Chapter 4 Problem in your book on pg 181). They used the MicroSort technique which increased their probability of having a girl to instead of the usual ½ Now find the probability of having exactly two girls. Again, let's start with the sample space and calculate and record the probabilities of each possible outcome in the table below. 1. POX) 211 3 (3 2)71 3) (3 GGB 3) 3 GBG BHAG GBB 31.33. 3) 3 2 BGG 3) (3 1)2 3) (3 BGB BBG 331.3 3) (3

Explanation / Answer

Solution :

Given,

probability of getting a girl = P( G ) = 2 / 3

probability of getting a boy = P( B ) = 1 / 3

( 2 )

Probability of getting exactly 2 girls = P( GGB ) + P( GBG ) + P( BGG) =  ( (2/3)*(2/3)*(1/3) )+ ( (2/3)*(1/3)*(2/3) ) +

  +  ( (1/3)*(2/3)*(2/3) )  

= 0.4444

( 3 )

probability of getting a boy , a girl and a girl = P(BGG) =  ( (1/3)*(2/3)*(2/3) )  

= 0.1481

( 4 )

N0, the probability does not change if we change the order

probability of getting a boy , a girl and a girl = P(GBG) =  ( (2/3)*(1/3)*(2/3) )  

= 0.1481

( 5 )

Total number of ways of gettin 3 children = 2*2*2 = 8

probability of getting any of the sequences i.e,, (BGG),(GBG),(GGB) = 3/ 8 = 0.3750

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