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Probability Ncert Solutions Maths class 12th Maths Class 12th Probability

78. A couple has two children.

(i) Find the probability that both children are males I it is known that at least one of the children is male.

(ii) Find the probability that both children are females if it is known that the elder child is a female.

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Answered by

alok kumar singh | Contributor-Level 10

4 months ago

78. i. Here, Sample space of given condition,

$S = {(B, B), (B, G), (G, B), (G, G)}$

Let, $E :$ denotes the event both children are male

$F :$ denotes the event at least one of the children is a male

$∴ E \cap F = {(B, B)}$

$\Rightarrow P (E \cap F) = \frac{1}{4}$

Here, $P (E) = \frac{1}{4}$ and $P (F) = \frac{3}{4}$

$\Rightarrow P (E / F) = \frac{P (E \cap F)}{P (F)} = \frac{\frac{1}{4}}{\frac{3}{4}} = \frac{1}{3}$

ii. Let, $A :$ event that both children are female

$B :$ event that elder child is female

$A = {G, G}$ $P (A) = \frac{1}{4}$

$B = {(G, G), (G, B)}$ $P (B) = \frac{2}{4} = \frac{1}{2}$

$A \cap B = {(G, G)}$ $P (A \cap B) = \frac{1}{4}$

$P (A / B) = \frac{P (A \cap B)}{P (B)}$

$= \frac{\frac{1}{4}}{\frac{1}{2}} = \frac{1}{4} \times 2 = \frac{1}{2}$

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P (2 obtained on even numbered toss) = k (let)

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P ( $\bar{2}$ )= $\frac{5}{6}$

$k = \frac{5}{6} \times \frac{1}{6} + {(\frac{5}{6})}^{3} \times \frac{1}{6} + {(\frac{5}{6})}^{5} \times \frac{1}{6} + . . .$

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If x = 0, y = 6, 7, 8, 9, 10

If x = 1, y = 7, 8, 9, 10

If x = 2, y = 8, 9, 10

If x = 3, y = 9, 10

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ax² + bx + c = 0

D = b² – 4ac

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(iii) AC = 9, b = 6, a = 3, c = 3 is one way

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78. A couple has two children.

(i) Find the probability that both children are males I it is known that at least one of the children is male.

(ii) Find the probability that both children are females if it is known that the elder child is a female.

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78. A couple has two children. (i) Find the probability that both children are males I it is known that at least one of the children is male. (ii) Find the probability that both children are females if it is known that the elder child is a female.

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78. A couple has two children.

(i) Find the probability that both children are males I it is known that at least one of the children is male.

(ii) Find the probability that both children are females if it is known that the elder child is a female.