two cards are drawn without replacement from an ordinary deck of 52 playing cards. what is the probability that both cards are kins if the first card drawn was a king?
I was thinking it was 13/51 but not sure.
How many kings are left?
is it three?
So proability for drawing 3 cards out of 51 left is....
4/52 *3/51 =1/221 that's the correct answer
To solve this problem, let's break it down step by step.
Step 1: Determine the number of kings in the deck.
There are a total of 4 kings in a standard deck of 52 playing cards.
Step 2: Determine the number of cards remaining after the first king is drawn.
Once the first king is drawn, there are 51 cards remaining in the deck.
Step 3: Determine the number of kings remaining after the first king is drawn.
Since there are 4 kings in the deck initially and one king has already been drawn, there are 3 kings remaining in the deck.
Step 4: Determine the number of ways to draw a king as the second card.
Since there are 3 kings remaining in the deck and 51 cards remaining overall, the number of ways to draw a king as the second card is 3.
Step 5: Calculate the probability.
The probability is given by the number of favorable outcomes (drawing two kings) divided by the number of possible outcomes (drawing any two cards).
Number of favorable outcomes = 3 (drawing a king as the second card)
Number of possible outcomes = 51 (drawing any two cards from the remaining deck)
Therefore, the probability that both cards are kings if the first card drawn was a king is:
Probability = Number of favorable outcomes / Number of possible outcomes
= 3 / 51
= 1 / 17
So, the correct probability is 1/17, not 13/51 as you initially thought.