Question

In a sequence of independent flips of a coin that comes up heads with a probability of 0.6, what is the probability that there is a run of three consecutive heads within the first 10 flips?

Answer 1

The probability of getting a run of three consecutive heads within the first 10 flips of a coin with a probability of 0.6 is 0.096.

Step-by-step explanation:

To calculate the probability of getting a run of three consecutive heads within the first 10 flips, we can use the concept of geometric distribution. The probability of getting a run of three consecutive heads is the same as getting a single success in a sequence of failures and successes. Since the probability of getting a head is 0.6, the probability of getting a tail is 1 - 0.6 = 0.4. Therefore, the probability of getting a run of three consecutive heads within the first 10 flips can be calculated as:

P(X = 1) = (0.4)^2 * 0.6 = 0.096