NCERT Class XII Mathematics Chapter - - Solutions
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Question : 12
Total: 101
Assume that each born child is equally likely to be a boy or a girl. If afamily has two children, what is the conditional probability that both aregirls given that (i) the youngest is a girl, (ii) at least one is a girl ?
Solution:
Let b denote the boy and g denote the girl.
S = {bb, bg, gb, gg} which contains four equally likely sample points.
E : ‘both children are girls’ ⇒ E = {gg} ⇒ P(E) = 1/4
(i) F : ‘the youngest is a girl’, then F = {bg, gg} ⇒ P(F) = 2/4
⇒ E ∩ F = {gg} ⇒ P(E∩F) = 1/4
∴ Required probability= P ( E | F ) =
=
=
(ii) F : ‘atleast one is a girl’, then F = {bg, gb, gg} ⇒ P(F) = 3/4
E ∩ F = {gg} ⇒ P(E∩F) = 1/4
∴ Required probability = P(E | F)=
=
=
S = {bb, bg, gb, gg} which contains four equally likely sample points.
E : ‘both children are girls’ ⇒ E = {gg} ⇒ P(E) = 1/4
(i) F : ‘the youngest is a girl’, then F = {bg, gg} ⇒ P(F) = 2/4
⇒ E ∩ F = {gg} ⇒ P(E∩F) = 1/4
∴ Required probability
(ii) F : ‘atleast one is a girl’, then F = {bg, gb, gg} ⇒ P(F) = 3/4
E ∩ F = {gg} ⇒ P(E∩F) = 1/4
∴ Required probability = P(E | F)
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