Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What is the probability that the second card is a number card, if the first card was a queen? The face cards are King, Queen, Jack. The number cards are ace – 10.

so there are 12 face cards and 40 number cards.

since the first card was a queen, the 40 facecards are still in the remaining 51 cards
prob = 40/51

Thanks!

To find the probability that the second card is a number card, given that the first card was a queen, we need to determine the number of favorable outcomes and the number of total outcomes.

First, let's find the number of favorable outcomes, which is the number of number cards left in the deck after drawing a queen. There are 4 queens in a deck, so after drawing one, there are 52 - 4 = 48 cards remaining.

Out of these remaining 48 cards, there are 36 number cards (4 aces, 4 twos, ..., 4 tens). Therefore, there are 36 favorable outcomes.

Now, let's find the number of total outcomes. After drawing the first card (a queen), there are 51 cards remaining in the deck. So, there are 51 possible outcomes for the second card.

Therefore, the probability of drawing a number card, given that the first card was a queen, is:

Probability = Favorable outcomes / Total outcomes

Probability = 36 / 51

Simplifying the fraction, we get:

Probability ≈ 0.706 (rounded to three decimal places)

So, the probability that the second card drawn is a number card, if the first card was a queen, is approximately 0.706.