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