Using the binomial distribution, the probability of flipping a coin 11 times and getting heads 4 times is:
A. 16.1%.
What is the binomial distribution formula?
The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
For this problem, considering a fair coin, that is, equally as likely to be heads or tails, the parameters are given by:
p = 0.5, n = 11.
The probability of 4 heads is P(X = 4), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{11,4}.(0.5)^{4}.(0.5)^{7} = 0.161[/tex]
Hence option A is correct.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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