These events are independent, so

$P(A' \text{ and } B') = P(A') \times P(B') = (1 - 0.15) \times (1 - 0.10) = 0.765 \text{ or } 76.5\%$

Explanation:

• Let A be the event that the male driver has a claim: P(A) = 0.15
• Let B be the event that the female driver has a claim: P(B) = 0.10
• The probability that the male driver does NOT have a claim: P(A') = 1 - 0.15 = 0.85
• The probability that the female driver does NOT have a claim: P(B') = 1 - 0.10 = 0.90
• Since the events are independent (the claim status of one driver doesn't affect the other), the probability that neither has a claim is: P(A' and B') = P(A') × P(B') = 0.85 × 0.90 = 0.765 = 76.5%