Determine if the events A and B are mutually exclusive, independent, or neither. P(A)=0.32, P(B)=0.4,P(A or B)=0.7
To determine if events A and B are mutually exclusive, independent, or neither, we need to consider the relationship between the probability of A, the probability of B, and the probability of both A and B occurring.
If events A and B are mutually exclusive, it means they cannot occur at the same time. In this case, P(A or B) would be equal to the sum of the probabilities of A and B since they cannot both occur simultaneously. However, we are given that P(A or B) = 0.7, which is not equal to P(A) + P(B) in this case. Therefore, events A and B are not mutually exclusive.
If events A and B are independent, it means the occurrence of one event does not affect the probability of the other event. In other words, P(A and B) = P(A) * P(B). Let's calculate the value of P(A and B).
P(A or B) = P(A) + P(B) - P(A and B)
0.7 = 0.32 + 0.4 - P(A and B)
0.7 = 0.72 - P(A and B)
P(A and B) = 0.72 - 0.7
P(A and B) = 0.02
Now let's check if P(A and B) is equal to P(A) * P(B).
0.02 = 0.32 * 0.4
0.02 = 0.128
Since 0.02 is not equal to 0.128, events A and B are not independent.
Therefore, the events A and B are neither mutually exclusive nor independent.