Question

The probability that a house will have a black mailbox is 71%. As a person wants to find the probability that 6 out of 10 houses will have a black mailbox. In words, define success for THIS problem.

Answer 1

In this problem, success is defined as 6 out of 10 houses having a black mailbox. We can solve this problem using the binomial probability formula.

Step-by-step explanation:

In this problem, success is defined as 6 out of 10 houses having a black mailbox. We can solve this problem using the binomial probability formula.

1. The probability of success (p) is 0.71.
2. The number of trials (n) is 10 (as there are 10 houses).
3. We want to find the probability of exactly 6 successes, so we use the combination formula: C(10, 6) = 210.
4. The probability of exactly 6 successes is then calculated as:
   P(X = 6) = C(10, 6) * (0.71)^6 * (1 - 0.71)^(10-6) = 0.1283.