Question

A coin is weighted so that there is a 61.2% chance of it landing on heads when flipped. The coin is flipped 15 times. Find the probability that the number of flips resulting in "heads" is at least 5 and at most 10 .

Answer 1

The probability of a weighted coin landing on heads between 5 and 10 times in 15 flips is calculated using the binomial probability formula, summing up each probability from 5 heads to 10 heads.

Step-by-step explanation:

To find the probability that a weighted coin with a 61.2% chance of landing on heads results in at least 5 and at most 10 heads when flipped 15 times, we would need to use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Where:

• n = number of trials (in this case, 15 flips)
• k = number of successful events (number of heads, varying from 5 to 10)
• p = probability of success on a single trial (61.2% or 0.612)
• q = probability of failure on a single trial (1 - p)

To solve this, you would calculate the probability for each value of k from 5 to 10 and sum those probabilities. This would give you the overall probability of getting between 5 and 10 heads inclusive.