Question

You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten.

Answer 1

Answer:

$\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%$

Step-by-step explanation:

There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.

At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just

$\frac{4}{52}$

After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is

$\frac{4}{51}$

Now to get the total probability we need to multiply the two probabilities together

$\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%$