Question

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.

Answer 1

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:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{3,3}.(0.5)^{3}.(0.5)^{0} = 0.125$

0.125 = 12.5% probability of observing exactly 3 tails.

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