Calculate the probability of getting 12 heads in 20 attempts from a fair coin. 0.120 0.240 0.280 0.301

To calculate the probability of getting 12 heads in 20 attempts from a fair coin, we can use the binomial probability formula, which is:

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

where:

• P(X=k) is the probability of k successes in n trials
• C(n, k) is the combination of n items taken k at a time
• p is the probability of success on a single trial (0.5 for a fair coin)
• n is the number of trials (20 in this case)
• k is the number of successes we want (12 in this case)

Step 1: Calculate C(n, k) C(20, 12) = 20! / [(20-12)! * 12!] = 125970

Step 2: Calculate p^k (0.5)^12 = 0.000244140625

Step 3: Calculate (1-p)^(n-k) (0.5)^(20-12) = 0.00390625

Step 4: Multiply the results of steps 1, 2, and 3 to get the final probability P(X=12) = 125970 * 0.000244140625 * 0.00390625 = 0.120134354

So, the probability of getting 12 heads in 20 attempts from a fair coin is approximately 0.120.