Answer:
c. 0.219
Step-by-step explanation:
If the coin is fair, then the probability of flipping a head is 1/2 = 0.5
Therefore, we can model this as a binomial distribution:
X ~ B(n, p) where n is the number of events and p is the probability of success
Given:
X ~ B(8, 0.5)
Using a calculator:
P(X = 5) = 0.21875 = 0.219 (3 dp)
Using the formula:
[tex]\sf P(X=x)=\dfrac{n!}{(n-x)!x!}p^x(1-p)^{n-x}[/tex]
(where n is the number of events, x is the number of desired successes and p is the probability of success)
[tex]\sf \implies P(X=5)=\dfrac{8!}{(8-5)!5!}0.5^5(1-0.5)^{8-5}[/tex]
[tex]\sf \implies P(X=5)=\dfrac{8!}{3!5!}0.5^50.5^3[/tex]
[tex]\sf \implies P(X=5)=56 \cdot 0.5^8[/tex]
[tex]\sf \implies P(X=5)=56 \cdot \dfrac{1}{256}[/tex]
[tex]\sf \implies P(X=5)=\dfrac{7}{32}[/tex]
[tex]\sf \implies P(X=5)=0.21875[/tex]
