Question

What is the probability of flipping a coin 8 times and getting heads 3 times?

Answer 1

I'm pretty sure the answer is D. 27.3%

because say you still flipped it 8 times but got heads 4 times, theres a 50% chance of that happening because there are two sides to the coin, you can pretty much just eyeball it from there.

Answer 2

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

$\left[\begin{array}{c}&n\\&r\end{array}\right] * H^{r} * T^{n - r}$

Where n = number of tosses = 8

r = number of heads

By Substitution,

$\left[\begin{array}{c}&n\\&r\end{array}\right] * H^{r} * T^{n - r}$ becomes

$\left[\begin{array}{c}&8\\&3\end{array}\right] * 0.5^{3} * 0.5^{8 - 3}$

$\frac{8!}{(8-3)!3!} * 0.5^{3} * 0.5^{8 - 3}$

$\frac{8 * 7 * 6 * 5!}{(5!!3!} * 0.5^{3} * 0.5^5$

$\frac{8 * 7 * 6 }{3 * 2} * 0.5^{3} * 0.5^5$

$8 * 7 * 0.5^{3} * 0.5^5$

= 0,21875

= 21.875%

= 21.9% --- Approximately