Question

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a face card for the second card drawn, if the first card, drawn without replacement, was a jack? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Sol : Given

Two cards are drawn from a standard deck of 52 cards without replacement

Probability of choosing a jack for the first card

Jack is 4 out of 52 cards

Probability that first card is jack = 4/52

One card is drawn there are 51 remaining in the deck

Probability that second card is a face card

There are 12 face cards total in the standard deck of cards

Therefore

Probability that the second card is a face card = 12/51

As there are 51 cards after first card is drawn

Probability that choosing a face card for the second card drawn,if the first card drawn without a replacement was a jack

= 4/52 * 12/51

= 48/2652

= 0.0180995475.