Question

Find the indicated Probability Given

P(A)=0.35
P(B)=0.25
P(A or B)=0.25
P(A and B)=______
​
Is this an overlapping or disjoint event.
A.overlapping
B.disjoint event.

Answer 1

There is likely an error in the given data, as the computed P(A and B) using the provided probabilities is illogical. Assuming the provided P(A or B) is correct, A and B are disjoint events, and P(A and B) = 0.

Step-by-step explanation:

The student is asking for the probability of the intersection of two events, A and B (P(A and B)), given the probability of each event occurring individually and the probability of either event occurring. The probabilities given are P(A) = 0.35, P(B) = 0.25, and P(A or B) = 0.25.

Using the formula for the probability of the union of two events, we have P(A or B) = P(A) + P(B) - P(A and B). We can rearrange this to find P(A and B):

P(A and B) = P(A) + P(B) - P(A or B) = 0.35 + 0.25 - 0.25 = 0.35. However, this result is illogical since it can't be greater than any individual probability, which signifies that the initial data provided may have an error. If we assume that the given probability for P(A or B) is correct, then the events A and B are disjoint events, which means they cannot occur simultaneously, and thus P(A and B) = 0.