GATE Overflow Test Series | Mock GATE | Test 5 | Question: 64

Question

In the city of Rebuke birth rate is uniform for all months except September where the number of births is double the normal. Also, $3$ girl children are born in September for every $2$ boy children where as the ratio is the same for every other month. Given then Kavya (assume female gender) is born in Rebuke what is the probability that her birthday is in September? (up to $3$ decimal places)

Answer 1

Let the probability of a birth being in any non September month be $x.$

We have $11x + 2x = 1 \implies x = 1/13.$

Probability of a girl child in September $\frac{3}{5}.$

Probability of girl child overall $ = \dfrac{2 \times \frac{3}{5} + 11 \times 0.5}{13} =0.5153 $

$P(Sep | F) = \dfrac{P(Sep \cap F)}{P(F)} = \dfrac{\frac{2}{13}.\frac{3}{5}}{0.5153} = 0.179.$

Comments

Jan → 10 Children (5G, 5B)

Feb → 10 Children (5G, 5B)

March → 10 Children (5G, 5B)

April → 10 Children (5G, 5B)

May → 10 Children (5G, 5B)

June → 10 Children (5G, 5B)

July → 10 Children (5G, 5B)

Aug → 10 Children (5G, 5B)

Sep → 20 Children (12G, 8B)

Oct→ 10 Children (5G, 5B)

Nov → 10 Children (5G, 5B)

Dec → 10 Children (5G, 5B)

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Required Prob. = 12/(12+5*11) = 0.179