Answer:
Explanation:
The probability of getting exactly 25 heads in 50 coin flips would be higher than flipping a coin 6 times and getting exactly 3 heads.
To understand why, we can use the formula for calculating the probability of getting a specific number of heads in a given number of coin flips, which is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where P(X=k) is the probability of getting exactly k heads, n is the total number of coin flips, p is the probability of getting heads on a single coin flip, and (n choose k) is the binomial coefficient.
For the first scenario of flipping a coin 50 times and getting exactly 25 heads, we can plug in the values and get:
P(X=25) = (50 choose 25) * 0.5^25 * 0.5^25 = 0.112
For the second scenario of flipping a coin 6 times and getting exactly 3 heads, we can similarly plug in the values and get:
P(X=3) = (6 choose 3) * 0.5^3 * 0.5^3 = 0.3125
As we can see, the probability of getting exactly 25 heads in 50 coin flips is much higher than the probability of flipping a coin 6 times and getting exactly 3 heads. This is because the probability of getting a single head on a coin flip is 0.5, and as the number of coin flips increases, the probabilities of different outcomes converge towards a bell-shaped distribution centered around 0.5. This means that the probability of getting a specific number of heads in a large number of coin flips becomes more likely as the number of coin flips increases.