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r2kins
07-17-2004, 07:02 PM
PROBABILITY QUESTIONS
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is:

1: either a black card or a king
2: neither a heart nor a king
3: spade or ace

Answers

1: 7/13
2: 9/13
3: 9/13

sri830
07-17-2004, 07:54 PM
1)

let A is an event of drawing black card and B is the event of drawing a king.
Probability of A = 26/52
Probability of B = 4/52
Probability of drawing a black card and king is 2/52

P(A or B) = P (A) + P(B) - P (A and B)

= 26/52 + 4/52 - 2/52 = 7/13

2)
let A is an event of not drawing a heart and B is the event of not selecting a king.
Probability of A = 39/52
Probability of B = 48/52
Probability of not selecting a heart and not selecting a king is = ( 1- probability of selecting a black heart king) = 1 - 1/52 = 51/52 (since we have only one black heart king)

P(A or B) = P (A) + P(B) - P (A and B)

= 39/52 + 48/52 - 51/52 = 9/13

3)
let A is an event of drawing spade card and B is the event of drawing an ace.
Probability of A = 13/52
Probability of B = 4/52
Probability of drawing a spade card and an ace is 1/52

P(A or B) = P (A) + P(B) - P (A and B)

= 13/52 + 4/52 - 1/52 = 4/13


Plzz check your answer again for third one....

arkham
07-18-2004, 03:41 AM
Yeah there's no way the third one is 9/13. It has to be 4/13. This question is basically asking for (1 - the answer to the second question).

Do the probability questions on the GRE get any harder than this?

r2kins
07-18-2004, 06:24 PM
Hi SRINI and thanks for the solutions !

You seem to have used the formula:

Probability of A OR B happening =
(sum of the individual probabilities of A and B ) – (probability of A AND B happening)


plz tell me I am right in arriving at this conclusion and whether the above formula has any exceptions to it?

As far as the third ques is concerned, your answer seems right, but….in the book it’s given as 9/13 only….maybe it’s a misprint.

r2kins
07-18-2004, 06:25 PM
hi arkham
As far as the level of probability questions on the GRE arises…your guess would be as good as mine!! But I think these are relatively easy and the ques on the real GRE may be a bit trickier!

sri830
07-18-2004, 06:49 PM
Yes. You are right r2kins. We also can solve this problem with common practical approach if you cannot remember the formula. Lets see the first question. That is probability of drawing either a black card or a king.
we know that the probability of drawing black card is 26/52. Probability of drawing a king is 4/52. when we draw a card from a pack of 52, the card could either be a black card or a king. But, what if we draw a card which is a black king? We already counted probability for drawing a black card or a king. So we have to substract the common probability of drawing a black card which is a king. We only have 2 black kings. so the probability is 2/52. we should deduct this from the total probability.

r2kins
07-19-2004, 05:29 PM
ya i understand it now....thanks

rashmi
09-28-2004, 12:14 PM
can someone please explain the second part again please?

Azzkikr6969
09-28-2004, 03:46 PM
can someone please explain the second part again please?
neither a heart nor a king. Heart has 13 cards and king has 4 cards. But king is already a heart. So there is a total of 13+4-1 = 16 cards that the user should not choose. The probability is then 1-16/52 = 36/52 = 9/13

rashmi
09-28-2004, 07:03 PM
thanks a ton.

sarahmahmoodkhan
12-12-2007, 07:02 PM
1.black cards=26 non black kings =2 26+2=28............P=28/52=7/13
2.total heart cards=13 non heart kings=3 13+3=16
remaining cards=52-16=36 P=36/52=9/13
3.spade cards=13 non spade aces=3 13+3=16 P=16/52=4/13