Question

In a family having three children there may be no girl ,one girl,two girl or three girl.so the probability of each is1/4 justify your answer

Answer 1

the four outcomes: no girl,1girl,2girl,3girls
in all the four cases the favourable outcome is one . so the probability of each outcome is 1/4

Answer 2

Solution :

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Given :

In a family having 3 children, to find the probablity of  no girls, 1 girl, two girls or 3 girls,.

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We know that,

Probablity of an event = Number of favourable outcomes/ Total number of possible outcomes

⇒ Hence, all the psossible outcomes (Number of girls in a family with 3 children) are as follows,.

Let B donates the probablity of getting a boy in a family,.

&

Let G donates the probablity of getting a girl in a family,.

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Hence, the possible out comes are :

 The order of birth :
                                   N(S)⇒ {B,B,B}  , {G,B,B} , {B,G,B} , {B,B,G} , {G,G,B} , {G,B,G} , {B,G,G} , {G,G,G},.

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⇒  Hence, the probability[P(A)] of getting no girl in a family  = number of favourable outcomes/ total number of possible outcomes = n(A) / n(S) = 1/8


⇒  Hence, the probability[P(B)] of getting a girl in a family  = number of favourable outcomes/ total number of possible outcomes = n(B) / n(S) = 3/8


⇒  Hence, the probability[P(C)] of getting two girls in a family  = number of favourable outcomes/ total number of possible outcomes = n(C) / n(S) =3/8


⇒  Hence, the probability[P(D)] of getting all three girls in a family  = number of favourable outcomes/ total number of possible outcomes = n(D) / n(S) = 1/8


May be, if order of birth doesn't matter,.

⇒ The possible outcomes are :

⇒ {0,3B} , {G, 2B} , {2G, B} , {3G, B}

Hence, probablity of each is 1/4,.


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