Answer:
The probability of flipping a coin 10 times and it landing on heads exactly seven times is about 0.1172 or 11.72%.
Step-by-step explanation:
We can use basic binomial distribution, which is given by the formula:
[tex]\displaystyle P(x) = {n \choose x}p^xq^{n-x}[/tex]
Where n represent the number of trials, x represent the number of successes desired, p represent the chance of success, and q represent the chance of failure.
Since we are flipping a coin 10 times, we are conducting 10 trials. So, n = 10.
We want to probability that it lands on heads exactly 7 out of 10 times. So, the number of desired successes x is 7.
The probability of success p is 1/2.
And the probability of failure q is also 1/2.
Substituting:
[tex]\displaystyle P(7)={10 \choose 7}\left(\frac{1}{2}\right)^7\left(\frac{1}{2}\right)^3=120\left(\frac{1}{2}\right)^{10}=\frac{120}{1024}=\frac{15}{128}\approx0.1172[/tex]
The probability of flipping a coin 10 times and it landing on heads exactly seven times is about 0.1172 or 11.72%.
