Question

Suppose you decided to keep flipping a coin until tails came up, at which

Answer 1

Answer:

B. 6.3%

Step-by-step explanation:

For each time that the coin is tosse, there are only two possible outcomes. Either it comes up tails, or it does not. The probability of coming up tails on a toss is independent of any other toss. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

Fair coin:

Equally as likely to come up heads or tails, so $p = 0.5$

Probability that the first tails comes up on the 4th flip of the coin?

0 tails during the first three, which is P(X = 0) when n = 3.

Tails in the fourth, with probability 0.5. So

$p = 0.5P(X = 0)$

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

$p = 0.5P(X = 0) = 0.5*(C_{3,0}.(0.5)^{0}.(0.5)^{3}) = 0.0625$

0.0625 * 100 = 6.25%

Rounding to the nearest tenth of a percent, the correct answer is:

B. 6.3%