# If a fair coin is tossed 10 times and the probability that it shows heads in the first four tosses and tail in last six tosses. - Mathematics and Statistics

Sum

If a fair coin is tossed 10 times and the probability that it shows heads in the first four tosses and tail in last six tosses.

#### 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(getting heads in first four tosses and tails in last six tosses) = P(X = 4)

= p(4) = "^10C_4 * (1/2)^10

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

= 210 xx 1/1024 = 105/512

Hence, the probability that getting heads in first four tosses and tails in last six tosses = 105/512.

Concept: Mean of Binomial Distribution (P.M.F.)
Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 8 Binomial Distribution
Miscellaneous exercise 8 | Q 3.2 | Page 253