Using binomial distribution, find the probability of getting 4 heads in 6 tosses of a fair coin.

Sure, here is the step by step solution:

Step 1: Identify the parameters of the binomial distribution. In this case, the number of trials n is 6 (the number of coin tosses), the number of successful outcomes k is 4 (the number of heads we want to get), and the probability of success on each trial p is 0.5 (since the coin is fair).

Step 2: Use the formula for the binomial probability, which is:

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

where C(n, k) is the number of combinations of n items taken k at a time, p is the probability of success, and (1-p) is the probability of failure.

Step 3: Calculate C(n, k). The formula for combinations is:

C(n, k) = n! / [k!(n-k)!]

where "!" denotes factorial. So, C(6, 4) = 6! / [4!(6-4)!] = 15.

Step 4: Substitute the values into the binomial probability formula:

P(X=4) = 15 * (0.5^4) * ((1-0.5)^(6-4)) = 15 * 0.0625 * 0.25 = 0.234375.

So, the probability of getting 4 heads in 6 tosses of a fair coin is approximately 0.234 or 23.4%.