Q76

[adekunle]

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!

 

[S2000magician]

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.

 

[adekunle]

Actually, it is the ”or both’ part that gave me 24%, plus the calculated 60% thus 84%. Why is this wrong?

 

[gunner.21]

Is the 40% prob P(A and B) or P(A given B)?

 

[S2000magician]

adekunle wrote:Actually, it is the ”or both’ part that gave me 24%, plus the calculated 60% thus 84%. Why is this wrong?

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%.

 

[S2000magician]

gunner.21 wrote:Is the 40% prob P(A and B) or P(A given B)?

Clearly that would make a difference.

 

[adekunle]

Thanks!

 

[S2000magician]

You’re welcome.