poker probability

• May 5th 2008, 05:23 PM
digitalis77
poker probability
A standard 52 card deck is well shuffled and the cards are drawn one at a time and without replacement until a king or queen is drawn. Determine the following probabilities.

a) What is the probability that at least 4 cards are drawn before the first king or queen occurs?

b) Given that a king or queen does not occur in the first 5 cards drawn, what is the probability that a king or queen occurs in 3 or fewer more draws?
• May 6th 2008, 12:31 AM
CaptainBlack
Quote:

Originally Posted by digitalis77
A standard 52 card deck is well shuffled and the cards are drawn one at a time and without replacement until a king or queen is drawn. Determine the following probabilities.

a) What is the probability that at least 4 cards are drawn before the first king or queen occurs?

This is the probability that none of the first four cards are a K or Q.

There are 44 cards which are not a K or Q

Thus the probability that the fiorst card is not a K or Q is 44/52
The probability that the second is not a K or Q is 43/51 (as after the first card is drawn there are 51 remaining of which 43 are not K or Q.

.. and so on for the third and fouth card.

The final probability is the product of the four probabilities you will have calculated.

Quote:

b) Given that a king or queen does not occur in the first 5 cards drawn, what is the probability that a king or queen occurs in 3 or fewer more draws?
After drawing 5 cards none of which are a K or Q, you have a deck with 47 cards of which 39 are not a K or Q.

The required probability here is 1 minus the probability that none of the first three cards is a K or Q. This klatter probability can be calculated using the technique of part (a).

RonL