Answered

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Suppose that an experiment consists of flipping a coin 3 times and observing the resulting sequence of heads and tails. Find the probability of observing: exactly 3 tails.

Sagot :

Using the binomial distribution, it is found that there is a 0.125 = 12.5% probability of observing exactly 3 tails.

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.

In this problem, considering 3 tosses of a fair coin, the parameters are n = 3 and p = 0.5.

The probability of 3 tails is P(X = 3), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.5)^{3}.(0.5)^{0} = 0.125[/tex]

0.125 = 12.5% probability of observing exactly 3 tails.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

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