A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?
Solution:
The binomial distribution formula is also written in the form of n-Bernoulli trials.
where nCx = n! / x!(n-x)!.
Hence,
P(x:n,p) = n! / [x! (n - x)! ]. px.(q)n - x
The tossing of a coin is a Bernoulli’s process which comprises ‘n’ Bernoulli trials and the probability of success in each trial is p and failure is q.
q is obtained by subtracting p (probability of success) from 1.
The probability of the desired outcome of an Bernoulli experiment which is given as follows:
P(X = x) = \( C_{x}^{n}\textrm{}q^{_{n-x}}p^{x}, x = 0,1, 2, .....n\)
The problem can be stated mathematically as n = 9 and x = 6 heads is
p = 1/2 ; q = 1 - 1/2 = 1/2
P(X = 6 heads) = \( C_{6}^{9}\textrm{}(1/2)^{_{9-6}}(1/2)^{6}, x = 0,1, 2, .....n \)
= (84) (1/2)3(1/2)6
= (84) (1/8) (1/64)
= 21/128
The probability of getting exactly 6 heads is 21/28.
A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?
Summary:
When a coin is tossed 9 times the probability of getting exactly six heads is obtained with the help of Bernoulli trials. The probability of getting exactly six heads is 21/128.
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