Question

If 2 cards are selected from a standard deck of 52 cards without replacement, find these probabilities. Both are the same suit.

Answer 1

4/17

Explanation:

There are 4 suits in the standard deck and 13 cards in each suit. The first pick doesn't matter as it doesn't specify which suit we need. Now that we have picked the first card, it will not be replaced, meaning there are now 51 cards, and importantly, only 12 cards left in the same suit as the one we picked. This means the probability that the next card we pick is in the same suit is 12 out of 51, or 12/51, which can be simplified to 4/17.

Answer 2

4/17

Explanation:

There are 52 cards in a standard deck.

There are 4 suits and 13 cards of each suit in a deck.

You select the first card, and it will be a card of one of the 4 suits.

Now you need to select a second card. You want it to be the same suit as the first card.

There are 51 cards left in the deck and 12 cards left of the same suit as the first card.

p(same suit) = 12/51 = 4/17