The probability of event A is 40%. The probability of event B is 60%, the joint probability of AB is 40%(how? I don’t know, subject of later discussion). The probability that A or B occurs, or both occur is closest to: A 84% B 40% C 60% My answer, 84%. Wrong apparently. Somebody help!
P(A or B) = P(A) + P(B) – P(AB)
= 40% + 60% – 40%
= 60%
Later discussion: as for why P(A) = P(AB):
P(AB) = P(B|A)P(A)
0.40 = P(B|A) × 0.40
P(B|A) = 1.0
Thus, if A happens, B is certain to happen. If you drew a Venn diagram, the circle for A would lie entirely inside the circle for B.
Actually, it is the '‘or both’ part that gave me 24%, plus the calculated 60% thus 84%. Why is this wrong?
Is the 40% prob P(A and B) or P(A given B)?
Probabilists use the phrase “A or B” to mean “A or B or both”.
I assume that you got the 24% by multiplying 40% by 60% (and that the 40% was P(A), not P(AB)). This calculation is correct only when A and B are independent; however, if they were, then P(AB) would be 24%.
Clearly that would make a difference.
Thanks!
You’re welcome.