CFA Practice Question

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CFA Practice Question

Roll a die and flip a coin, P(5 given heads) = ______.

A. 1/2
B. 1/6
C. 1/8
Correct Answer: B

Because these events are independent events (what happens with the coin has no effect on what happens with the die), P(5 | heads) = P(5). Now, roll a die P(5) = 1/6. So, P(5 | heads) = 1/6.

User Contributed Comments 12

User Comment
leoo how, i thought the question is what is the probabilty of rolling a 5 + head on the flip , shouldn't it be 1/6 * 1/2?
cfaman The questions asks the conditional probability. As the two events are independent, you can discard the condition so it's simply P(5) = 1/6.
Pooh cfaman, I believe you meant to say unconditional probability?
yanpz To Pooh, no, it's conditional probability. Actually for this question rolling a die won't affect the probability of flip coin, so the conditional probability value is the same as unconditional probability for given rolling die number, flip a coin.
tssverma tricky question. The question implicitly expects the reader to understand the coin tossing and rolling a die that they are mutually exclusive. Normally questions are more clear.
PeterW2006 P(5 and Heads) = P(5 | Heads) x P(Heads)
P(5 and Heads) = P(5) x P(Heads)
= 1/6 x 1/2
= 1/12
P(Heads) = 1/2
1/12 = P(5 | Heads) x 1/2
P(5 | Heads) = 1/6
mtcfa Even if you work out the whole problem utilizing the joint probability formula [ P(5!H) = P(5H)/P(H)], you still get 1/6. But if you can just see that they are independent events, you know the answer.
faya mtcfa:
But P(5H)=1/6=0.1667 and P(H)=0.5
So P(5H)/P(5)=0.1667/0.5=0.3333 which is not equal to 0.1667.

If they say P(5 given Heads) are we not to assume conditional prob - I'm confused.
adenisov PeterW2006:
without calculations
P(5 and Heads) = P(5 | Heads) x P(Heads)
P(5 and Heads) = P(5) x P(Heads)

so P(5 | Heads) x P(Heads) = P(5) x P(Heads)
and P(5 | Heads) = P(5)
StanleyMo i believe given is the key word, when talking about given, you need to determine yourself whether they are "dependant" or "independant".
maciejf Given is a very key word, we know that one event happend, so we have to count only probablility of rolling a die and having 5.
rsanfo Even if you think it is conditional, you get the same answer:
P(5|H) = P(5H) / P(H) = 1/12 divided by 1/2 = 1/6
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