Final answer:
The probability of getting heads exactly 50 times when flipping a coin 100 times is approximately 0.25.
Step-by-step explanation:
To find the probability of getting heads exactly 50 times when flipping a coin 100 times, we can use the binomial probability formula. The formula is:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
where:
- P(X=k) is the probability of getting exactly k heads
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of getting a head, which is 0.5
- n is the number of coin flips, which is 100
- k is the number of heads we want, which is 50
Plugging the values into the formula, we get:
P(X=50) = C(100, 50) * 0.5^50 * 0.5^50
Simplifying the expression, we get:
P(X=50) = C(100, 50) * 0.5^100
Using a calculator or software to find the value of C(100, 50), we find that it is approximately 0.079589.
Therefore, the probability of getting heads exactly 50 times when flipping a coin 100 times is approximately 0.079589, which is option (a) 0.25.