Final answer:
The probability of getting 7 or fewer heads when flipping a coin 13 times is approximately 0.682.
Step-by-step explanation:
To find the probability of getting 7 or fewer heads when flipping a coin 13 times, we need to calculate the probability of getting 0, 1, 2, 3, 4, 5, 6, or 7 heads. Each flip of a fair coin has a 50% chance of landing heads or tails, so the probability of getting a specific number of heads is calculated using the binomial probability formula.
The probability of getting exactly k heads in n flips is given by the formula:
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 getting a head (0.5 for a fair coin), and n is the number of flips.
For the given problem, the probability of getting 7 or fewer heads in 13 flips can be calculated as:
P(X≤7) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7)
By plugging in the values into the formula and calculating the probabilities for each number of heads, we find that the probability of getting 7 or fewer heads is approximately 0.682.