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 is ans. 0.77 none 0.92 0.48
Question
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 is ans. 0.77
none
0.92
0.48
Solution
The problem can be solved by using 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 (i.e., they can both occur).
Given: P(A) = Probability that the problem will be solved by a statistics student = 0.80 P(B) = Probability that the problem will be solved by a mathematics student = 0.60
We need to find P(A U B), the probability that the problem will be solved by at least one of the students.
However, we don't know P(A ∩ B), the probability that the problem will be solved by both students.
Assuming the worst case scenario, that is, the students never solve the problem together, we can say P(A ∩ B) = 0.
So, P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.80 + 0.60 - 0 = 1.40
But, the probability cannot be more than 1. Therefore, the maximum probability that at least one student will solve the problem is 1 or 100%.
So, none of the given options are correct.
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