Question

Let two cards be dealt successfully. without replacement, from a standard 52- card deck. Find the probability of the event. The first card is a jack and the second is a ten. The probability that the first card is a jack and the second card is a ten is

Answer 1

Two events are happening in this problem. Let's take a look first at the probability of getting a jack in a standard 52 card deck. There are 4 jacks present in the 52 card deck, hence, the probability of getting jack is

$P(jack)=\frac{4}{52}=\frac{1}{13}$

After one jack was drawn, there are 51 cards remaining in the deck. There are 4 ten cards present in the deck, hence, the probability for this will be

$P(ten)=\frac{4}{51}$

To get the overall probability of getting a jack on the first draw and ten on the second draw, just multiply the probabilities above. We get

$P=\frac{1}{13}\cdot\frac{4}{51}=\frac{4}{663}$

The answer to this problem is 4/663.