The conversation between human and AI assistant.
If two coins are tossed 5 times, what is the chance that there will be 5 heads and 5 tails?
Can you explain how you calculate the probability?
Sure! To calculate the probability of getting 5 heads and 5 tails when two coins are tossed 5 times, we can use the binomial probability formula. The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success, and (n choose k) is the binomial coefficient. For our case, n=10, k=5, p=0.5, and (n choose k) = 252. Plugging these values into the formula, we get P(X=5) = 252 * 0.5^5 * 0.5^5 = 0.2461.