# If fair coin is tossed 10 times and the probability that it shows heads 5 times. - Mathematics and Statistics

Sum

If a fair coin is tossed 10 times and the probability that it shows heads 5 times.

#### Solution

Let, X = number of heads.

p = probability that coin tossed shows a head

∴ p = 1/2

q = 1 - q = 1 - 1/2 = 1/2

Given: n = 10

∴ X ~ B (10, 1/2)

The p.m.f. of X is given by

P(X = x) = "^nC_x  p^x  q^(n - x)

∴ p(x) = ""^10C_x (1/2)^x (1/2)^(10 - x) = "^10C_x (1/2)^10, x = 0, 1, 2,...,10

P(coin shows heads 5 times) = P[X = 5]

= p(5) = "^10C_5 * (1/2)^10

= (10!)/(5! * 5!) xx 1/1024

= (10 xx 9 xx 8 xx 7 xx 6 xx 5!)/(5! xx 5 xx 4 xx 3 xx 2 xx 1) xx 1/1024 = 63/256

Hence, the probability that can shows heads exactly 5 times = 63/256.

Concept: Variance of Binomial Distribution (P.M.F.)
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 8 Binomial Distribution
Miscellaneous exercise 8 | Q 3.1 | Page 253