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)=(4)/(52)=(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)=(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=(1)/(13)\cdot(4)/(51)=(4)/(663)`

The answer to this problem is 4/663.