Answer:
The probability of flipping a coin 8 times and getting heads 3 times is 21.9%
Step-by-step explanation:
Given
A coin
A coin has two sides (a head and a tail)
The probability of getting a head is equal to the probability of getting a tail;
Let these probabilities be represented by H and P;
i.e. H = Probability of getting a Head
T = Probability of getting a Tail
Since both probabilities are equal and probability always sum to 1 then
H + T = 1
H + H = 1
2H = 1
H = 0.5 and T = 0.5
P (3 heads in 8 tosses) is given by the binomial representation
[tex]\left[\begin{array}{c}&n\\&r\end{array}\right] * H^{r} * T^{n - r}[/tex]
Where n = number of tosses = 8
r = number of heads
By Substitution,
[tex]\left[\begin{array}{c}&n\\&r\end{array}\right] * H^{r} * T^{n - r}[/tex] becomes
[tex]\left[\begin{array}{c}&8\\&3\end{array}\right] * 0.5^{3} * 0.5^{8 - 3}[/tex]
[tex]\frac{8!}{(8-3)!3!} * 0.5^{3} * 0.5^{8 - 3}[/tex]
[tex]\frac{8 * 7 * 6 * 5!}{(5!!3!} * 0.5^{3} * 0.5^5[/tex]
[tex]\frac{8 * 7 * 6 }{3 * 2} * 0.5^{3} * 0.5^5[/tex]
[tex]8 * 7 * 0.5^{3} * 0.5^5[/tex]
= 0,21875
= 21.875%
= 21.9% --- Approximately
