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:
[tex]n = 5[/tex] ---- number of flips
[tex]r = 2[/tex] ------ number of tails
First, we calculate the sample size (S)
[tex]S =r^n[/tex]
[tex]S =2^5[/tex]
[tex]S= 32[/tex]
Next, calculate the number of occurrence of 2 tails in 5 flips
This is calculated using the following combination formula
[tex]^nC_r = \frac{n!|}{(n - r)!r!}[/tex]
So, we have:
[tex]^5C_2 = \frac{5!|}{(5 - 2)!2!}[/tex]
[tex]^5C_2 = \frac{5!|}{3!2!}[/tex]
Expand
[tex]^5C_2 = \frac{5 \times 4 \times 3!|}{3! \times 2 \times 1}[/tex]
[tex]^5C_2 = \frac{20}{2 }[/tex]
[tex]^5C_2 = 10[/tex]
The probability is then calculated as:
[tex]P =\frac{^5C_2}{S}[/tex]
[tex]P =\frac{10}{32}[/tex]
Simplify
[tex]P =\frac{5}{16}[/tex]
Hence, the probability that you will get exactly 2 tails is 5/16
Read more about probabilities at:
https://brainly.com/question/11234923
