Question

A fair coin is flipped 10 times. What is the probability of obtaining exactly 7 heads when a fair coin is flipped 10 times? (Round your answer to three decimal places.)

PLEASE SHOW DETAILED EXPLANATION. Thank you! :)

Answer 1

The probability of getting exactly 7 heads in 10 flips of a fair coin is calculated using the binomial probability formula, resulting in approximately 0.117 when rounded to three decimal places.

Step-by-step explanation:

The probability of getting exactly 7 heads when a fair coin is flipped 10 times can be calculated using the binomial probability formula:

P(X = k) = C(n, k) × p^k × (1-p)^(n-k)

1. C(n, k) is the combination of n things taken k at a time.
2. p is the probability of getting a head on a single flip.
3. k is the number of heads we want to achieve, which is 7 in this case.
4. n is the total number of flips, which is 10.

Since the coin is fair, p = 0.5. Using these values, you can calculate the probability:

P(X = 7) = C(10, 7) × (0.5)^7 × (0.5)^(10-7)

C(10, 7) can be computed as 10!/(7! × (10-7)!), which is 120.

Therefore, P(X = 7) = 120 × (0.5)^7 × (0.5)^3

This simplifies to:

P(X = 7) = 120 × (0.5)^10

P(X = 7) = 120 × (1/1024)

P(X = 7) = 0.117188

Finally, rounding the probability to three decimal places gives us:

P(X = 7) ≈ 0.117