Questions: Check my work All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is 0.75 , the probability the second truck is available is 0.50 , and the probability that both trucks are available is 0.30 . points What is the probability neither truck is available? Note: Round your answer to 2 decimal places. eBook Probability

Solution Steps

To find the probability that neither truck is available, we can use the principle of complementary probability. First, calculate the probability that at least one truck is available by using the formula for the union of two events. Then, subtract this probability from 1 to find the probability that neither truck is available.

We are given the following probabilities:

• \( P(A) = 0.75 \) (the probability that the first truck is available)
• \( P(B) = 0.50 \) (the probability that the second truck is available)
• \( P(A \cap B) = 0.30 \) (the probability that both trucks are available)

To find the probability that at least one truck is available, we use the formula for the union of two events: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Substituting the values: \[ P(A \cup B) = 0.75 + 0.50 - 0.30 = 0.95 \]

The probability that neither truck is available is the complement of the probability that at least one truck is available: \[ P(\text{neither}) = 1 - P(A \cup B) \] Substituting the value we calculated: \[ P(\text{neither}) = 1 - 0.95 = 0.05 \]

Final Answer