Suppose the probability that a flight is on time is $P(ext\{on\; time\})\; =0.70$, the probability that it is less than $5$ minutes late is $P(ext\{less\; than\; \}5ext\{\; min\; late\})\; =0.15$, and the probability that it is more than $5$ minutes late is $P(ext\{more\; than\; \}5ext\{\; min\; late\})\; =0.15$. What is the probability that the flight will be no more than $5$ minutes late (to 2 decimals)?

• A. $0.85$
• B. $0.15$
• C. $0.30$
• D. $0.70$

Answer: (A)

Verified step by step guidance

1. Identify the events and their probabilities given in the problem: the probability that a flight is on time is \$0.70\(, the probability that it is less than 5 minutes late is \)0.15\(, and the probability that it is more than 5 minutes late is \)0.15$.
2. Understand that "no more than 5 minutes late" means the flight is either on time or less than 5 minutes late. So, this event includes both the "on time" and "less than 5 minutes late" probabilities.
3. To find the probability that the flight is no more than 5 minutes late, add the probabilities of the flight being on time and being less than 5 minutes late: \(P(\text{no more than 5 minutes late}) = P(\text{on time}) + P(\text{less than 5 minutes late})\).
4. Substitute the given values into the equation: \(P(\text{no more than 5 minutes late}) = 0.70 + 0.15\).
5. Sum these probabilities to get the final probability that the flight will be no more than 5 minutes late.