The local weather forecast indicates that there is a 60% chance of rain on Saturday and a 70% chance of rain on Sunday. A student concludes that there is a 130% chance of rain over the weekend. This is obviously not possible since it is over 100%. Explain clearly why the student's reasoning is incorrect.

The student is incorrect because the events are independent rather than mutually exclusive events.

Step-by-step explanation:

The student got a probability of 130% because he thought the probabilities are mutually exclusive. Since rain cannot fall on both Saturday and Sunday at the same time, they are independent. For mutually exclusive events, the probability that one or the other occurs is P(A or B) = P(A) + P(B).

Substituting P(A) and P(B), we have P(A or B) = P(A) + P(B) = 0.6 + 0.7 = 1.3 = 130 %.

But the probabilities are independent since Saturday and Sunday are two different days on the weekend and the probability of it raining on Saturday does not affect the probability of it raining on Sunday. Both events are independent.

For independent events A and B, the probability that both occurs is P(A and B) = P(A) × P(B), where P(A) is the probability of event A occurring and P(B) is the probability f event B occurring.

Let probability of it raining on Saturday = P(A) = 60% = 0.6 and probability of it raining on Sunday = P(A) = 70% = 0.7.

So, probability of it raining over the weekend is P(A and B) = P(A) × P(B) = 0.6 × 0.7 = 0.42 = 42%