Question

11.3.47 Q13 Let two cards be dealt​ successively, without​ replacement, from a standard​ 52-card deck. Find the probability of the event. The first card is a ten and the second is a jack. The probability that the first card is a ten and the second is a jack is

Answer 1

Let two cards be dealt successively, without a replacement, from a standard 52 card deck.

To find the chance that the first card is a ten, and the second is a jack.

Now, from 52 cards, 2 cards can be drawn successively, without replacement in 52*51 number of ways, because from the deck, the first card can be drawn in 52 ways and for any of them, the second can be drawn in 51 ways.

So, all possible cases is 52*51.

Now, in a standard deck, there are 13 denominations in 4 suits each.

So, there are 4 tens, and 4 jacks, as both a ten and a jack is a denomination.

So, the first card can be a ten in 4 ways, and for any of them, the second can be a jack in 4 ways.

So, the number of favourable cases is 4*4.

Thus, the required probability is

=(4*4)/(52*51)

=0.0060.

So, the probability that the first card ia a ten and the second is a jack is 0.0060.