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Solve the following problem : If a fair coin is tossed 4 times, find the probability that it shows head in the first 2 tosses and tail in last 2 tosses. - Mathematics and Statistics

Sum

Solve the following problem :

If a fair coin is tossed 4 times, find the probability that it shows head in the first 2 tosses and tail in last 2 tosses.

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Solution

Let X denote the number of heads.

P(getting head) = p = `(1)/(2)`

∴ q = 1 – p = `1 - (1)/(2) = (1)/(2)`

Given, n = 4

∴ X ∼ B`(4, 1/2)`
The p.m.f of X is given by

P(X = x) = `""^4"C"_x (1/2)^x (1/2)^(4 - x), x` = 0, 1,....,4

P(getting head in the first 2 tosses and tail in last 2 tosses.)

= `(1/2)^2 (1/2)^2`

= `(1)/(2^4)`

= `(1)/(16)`.

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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Part II | Q 1.03 | Page 156
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