Max picks two different cards without replacement from a standard 52-card deck. What is the probability that the cards are of different suits?
the first card has to be some suit.
That means that the 2nd card must be one of the 12 remaining cards of that suit. How many cards are left for the 2nd draw?
To find the probability that the two cards are of different suits, we first need to determine the total number of possible outcomes. In this case, Max selects two cards without replacement, which means once a card is selected, it is not put back into the deck before the second card is chosen.
Step 1: Find the total number of possible outcomes
For the first card, Max can choose any of the 52 cards. However, for the second card, there will only be 51 cards remaining in the deck to choose from.
Total number of possible outcomes = 52 * 51
Step 2: Find the number of favorable outcomes
Now we need to determine the number of favorable outcomes, where the two cards are of different suits.
There are four suits in a deck: hearts, diamonds, clubs, and spades. For the first card, Max can choose any of the 52 cards. However, for the second card, only 39 cards of different suits will be remaining in the deck (since there are 13 cards of each suit).
Number of favorable outcomes = 52 * 39
Step 3: Calculate the probability
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (52 * 39) / (52 * 51)
Simplifying the above expression, we get:
Probability = 39 / 51 = 13 / 17
So, the probability that the two cards drawn are of different suits is 13/17.