A fair coin is tossed 20 times. Let X be the number of heads thrown in...

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A fair coin is tossed 20 times. Let X be the number of heads thrown in...

A fair coin is tossed 20 times. Let X be the number of heads thrown in the first 10 tosses, and let Y be the number of heads tossed in the last 10 tosses. Find the conditional probability that X = 6, given that X + Y = 10.

math Statistics-And-Probability

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Answer 1

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Answer #1

X and Y are independent as outcome in first 10 tosses are independent of the outcome in last 10 tosses.

Y ~ Binomial( n = 10, p = 0.5)

The probability mass function of Y is

P(Y = y) = * 0.5% * (1-0.5) 10-у. У = 0. 1. 2. 3. 10

Now,

P(X 6)

P(X 6) since X and Y are independent

Rightarrow P(X + Y = 10 | X = 6) = P( Y = 4)

10 4 * 0.5% (1-0.5)10-4

Ply y) = 0.205078 (ans)

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Answer 2

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