Final answer:
To find the probability of getting heads no more than 5 times in 16 tosses of a weighted coin with a probability of 0.472 for heads, we can use the binomial probability formula.
Step-by-step explanation:
To find the probability of getting heads no more than 5 times in 16 tosses of a weighted coin with a probability of 0.472 for heads, we can use the binomial probability formula.
Let X be the random variable representing the number of heads. The probability of getting heads exactly k times out of n trials is given by:
P(X=k) = C(n, k) * p^k * q^(n-k)
where C(n, k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items. In this case, n=16, p=0.472, and q=1-p=0.528.
Now, we can calculate the probability of getting heads no more than 5 times:
- P(X=0) = C(16, 0) * (0.472)^0 * (0.528)^(16-0)
- P(X=1) = C(16, 1) * (0.472)^1 * (0.528)^(16-1)
- P(X=2) = C(16, 2) * (0.472)^2 * (0.528)^(16-2)
- P(X=3) = C(16, 3) * (0.472)^3 * (0.528)^(16-3)
- P(X=4) = C(16, 4) * (0.472)^4 * (0.528)^(16-4)
- P(X=5) = C(16, 5) * (0.472)^5 * (0.528)^(16-5)
Finally, we sum up these probabilities:
P(X ≤ 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)