I'm not sure if I'm doing this right.
Determine whether events A and B are independent.
P(A) =.5, P(B)= .7, P(AUB)= .85
P(AUB) = P(A) + P(B) - P(A∩B)
.5 +.7 - P(A∩B)
1.2-0.18=1.02
*0.18 because I solved for P(A∩B) in the previous question.
To determine whether events A and B are independent, we need to compare the probability of their intersection, P(A∩B), to the product of their individual probabilities, P(A) * P(B).
In your question, you mentioned that P(A) = 0.5, P(B) = 0.7, and you previously solved for P(A∩B) as 0.18.
To check for independence, calculate P(A) * P(B):
P(A) * P(B) = 0.5 * 0.7 = 0.35
Now compare this value to P(A∩B) = 0.18:
0.35 and 0.18
Since P(A) * P(B) = 0.35 is not equal to P(A∩B) = 0.18, we can conclude that events A and B are dependent, rather than independent.