Question

The complement of an event is all possible outcomes not in the event.

For example: If A = at least 3 girls are born to a family with 6 kids.

Then A' = A compliment is what happens if there are not at least 3 girls = less than 3 girls born to the family.

A useful formula: P(A) + P(A' ) = 1 or P(A') = 1 - P(A).

If P(x>5) = 0.028, what is P(x≤5)?

Answer 1

To find the probability of the complement event P(x≤5), subtract the given P(x>5) from 1, resulting in P(x≤5) = 0.972.

Step-by-step explanation:

The student's question relates to the complement of an event in probability. The complement of event A, denoted as A', consists of all possible outcomes that are not in A. According to probability theory, the sum of the probabilities of an event and its complement is equal to 1. Therefore, if P(x>5) is given as 0.028, then the probability of its complement, P(x≤5), can be found by subtracting P(x>5) from 1.

To calculate P(x≤5), we use the formula:

P(A') = 1 - P(A)

Substituting the given values:

P(x≤5) = 1 - P(x>5)

P(x≤5) = 1 - 0.028

P(x≤5) = 0.972

Thus, the probability that x is less than or equal to 5 is 0.972.