Question

When a biased coin is thrown 3 times, the probability of getting 3 tails is 27/125

Answer 1

Using the binomial distribution, it is found that the probability of getting 3 heads is of $\frac{8}{125}$.

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, we have that when n = 3, $P(X = 3) = \frac{27}{125}$, hence:

$p^3 = \frac{27}{125}$

$p = \sqrt[3]{\frac{27}{125}}$

$p = \frac{3}{5}$

The probability of 3 heads is P(X = 0), hence:

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

$P(X = 0) = C_{3,0}.\left(\frac{3}{5}\right)^{0}.\left(\frac{2}{5}\right)^{3} = \frac{8}{125}$

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

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