Question

If you flip a fair coin 5 times, what is the probability that you will get exactly 2 tails?

Answer 1

The answer will be 40%

Answer 2

Probabilities are used to determine the outcome of events

The probability that you will get exactly 2 tails is 5/16

From the question, we have:

$n = 5$ ---- number of flips

$r = 2$ ------ number of tails

First, we calculate the sample size (S)

$S =r^n$

$S =2^5$

$S= 32$

Next, calculate the number of occurrence of 2 tails in 5 flips

This is calculated using the following combination formula

$^nC_r = \frac{n!|}{(n - r)!r!}$

So, we have:

$^5C_2 = \frac{5!|}{(5 - 2)!2!}$

$^5C_2 = \frac{5!|}{3!2!}$

Expand

$^5C_2 = \frac{5 \times 4 \times 3!|}{3! \times 2 \times 1}$

$^5C_2 = \frac{20}{2 }$

$^5C_2 = 10$

The probability is then calculated as:

$P =\frac{^5C_2}{S}$

$P =\frac{10}{32}$

Simplify

$P =\frac{5}{16}$

Hence, the probability that you will get exactly 2 tails is 5/16

Read more about probabilities at:

https://brainly.com/question/11234923