CFA Practice Question

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CFA Practice Question

Two cards are randomly selected, without replacement, from a standard deck of playing cards. What is the probability of first picking a five and then picking a card other than a five?

A. 0.071
B. 0.004
C. 0.072
Correct Answer: C

p = (4/52) x (48/51) = 0.072398

User Contributed Comments 15

User Comment
eejo 4/52 x 48/51 = 192/2652 = .072
adenisov for all situation relating P(B|A):
we could say, than there is not "after taking 5", but situation C where just working with deck without on "5". Such we will have two independent outcomes.
Ildy can anyone care to explain why 48/51 and not 48/52?
Ildy the first card is not replaced :-) now i see it :-)
Daddykay P(picking a five the first time)=4/52.
Since it is not replaced we now have 51 cards remaining. There are a total of 48 (52-4) cards in the pile that are not-five. Therefore if he makes another pick P(not five)=48/51. You now multiply 4/52*48/51
Welles Why are the odds of picking a 5 the first go round 4/52 and not 4/48 (like from the question in the previous section regarding the odds of selecting a king being 4/48...chances for success/chances for failure)?
sogah look i dont play cards so quit using such examples
GouldenOne This says you have a 7 percent chance of drawing to 5's... im not buying it
GouldenOne Can someone explain the 48/51? The second time around there are 48 5's and not 3?
banihas A deck of cards has 52 total cards including four 5's. Now if we take one 5 out and do not replace it we are left with only three 5's left and a total of 51 cards remaining. Thus the probability of not picking a 5 from the deck of 51 remaining is 48/51 . Hence the probability of picking a card other than 5 GIVEN first picking a 5 is 4/52 * 48/51 = 0.072
fkigundu1 Got it at last
dbedford General Formula is P(BA) = P(A)P(B|A) where P(A) = picking a 5 first time = 4/52 and P(B|A) = Not picking a 5 Given that you picked a 5 the first time = 48/51.

The key is knowing that you are solving for P(BA) which is them saying AND, at least that's how I figured it out
Zhenek That feeling when I assume that the standard deck is 36 cards and not 52 ...
zhefuli I thought playing cards contain 2 jokers? So it'd be 54 cards right?
MathLoser I don't even know there are 52 cards in a deck.
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