There are 80% chance that a problem will be solved by a statistics student and 60% chance that the same problem will be solved by a mathematics student . The probability that at least the problem will be solved i

To solve this problem, we need to use the formula for the probability of the union of two events, which is P(A U B) = P(A) + P(B) - P(A ∩ B).

Here, the events A and B are not mutually exclusive because they can both occur (both students can solve the problem). However, we don't know the probability of A ∩ B (both students solving the problem), so we'll assume the worst case scenario where A and B are independent events. In this case, P(A ∩ B) = P(A) * P(B).

1. First, let's define our events:

   • Event A: The problem is solved by the statistics student.
   • Event B: The problem is solved by the mathematics student.

2. Next, let's plug in the given probabilities:

   • P(A) = 0.80 (80% chance the statistics student will solve the problem)
   • P(B) = 0.60 (60% chance the mathematics student will solve the problem)

3. Now, let's calculate P(A ∩ B):

   • P(A ∩ B) = P(A) * P(B) = 0.80 * 0.60 = 0.48

4. Finally, let's calculate P(A U B):

   • P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.80 + 0.60 - 0.48 = 0.92

So, there is a 92% chance that at least one of the students will solve the problem.