Easy Probablity

[garbage100]

Two cards are drawn at random from a standard deck of
52 cards, without replacement. What is the probability of
drawing a 7and a king in that order?

Basically I am confused, whether the answer should be:

a. (4/52) * (4/51)

or

b. (4C1*4C1)/ (52C2)

which one is wrong and why? I am struggling with probablity basics...bear with me :-)

[jimbob77]

A is correct. Not sure what your "C" refers to in B.

It is dependent probability. Chances of pulling a 7 = 4/52; chance of then pulling a king = 4/51

4/52 * 4/51 = 1/166

[sdasar]

In the fisrt option, cards are taken out in sequence and the first one is 7 and the second one is King. So we are looking for sequence 7-K. In this choice, the order is important.
Therefore the probability is (4C1 * 4C1) / 52P2 = 4 * 4 / 52 * 51


The second choice is where two cards are taken and we expect one card to be 7 and the other to be King. Here two sequences are possible 7-K and K-7. Since each (7K , K7) have the same probability, this option has twice probability when compared to the first one. Since in this option order is not important, the probability is (4C1*4C1) / 52C2 = 4 * 4 / (52 * 51 / 2).

[garbage100]

Thanks sdasar.you are awesome!! now i got it.