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Ex 13.1, 12 - If a family has two children. what conditional - Ex 13.1

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  1. Chapter 13 Class 12 Probability
  2. Serial order wise
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Ex 13.1, 12 Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl A family has 2 children Let girls be denoted by ‘g’ & boys be denoted by ‘b’ S = {(g, g), (g, b), (b, g), (b, b)} We need to find the Probability that both the children are girls, given that the youngest is a girl. Let F : youngest child in a girl E : both the children are girls We need to find P(E|F) Also, E ∩ F = {(g, g)} So, P(E ∩ F ) = 1﷮4﷯ Now, P(E|F) = 𝑃(𝐸 ∩ 𝐹)﷮𝑃(𝐹)﷯ = 1﷮4﷯﷮ 1﷮2﷯﷯ = 1﷮4﷯ × 2﷮1﷯ = 𝟏﷮𝟐﷯ Ex 13.1, 12 Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (ii) at least one is a girl? S = {(g, g), (g, b), (b, g), (b, b)} We need to find the probability that the children are girls, given that at least one is a girl. F : at least one child is a girl E : both the children are girls Also, E ∩ F = {(g, g)} So, P(E ∩ F ) = 1﷮4﷯ Now, P(E|F) = 𝑃(𝐸 ∩ 𝐹)﷮𝑃(𝐹)﷯ = 1﷮4﷯﷮ 3﷮4﷯﷯ = 1﷮4﷯ × 4﷮3﷯ = 1﷮3﷯ ∴ P(E|F) = 𝟏﷮𝟑﷯

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