Two cards are drawn without replacement from a deck of 52 cards. What is the probability that both are tens, if the first card was a ten?
probably 1/10
There are 3 tens in the remaining 51 cards = 3/51
To calculate the probability, we need to determine the number of desired outcomes (getting two tens) and the total number of possible outcomes.
First, let's find the number of desired outcomes. Since the first card was already drawn and it was a ten, there are 3 remaining tens in the deck. Therefore, the number of desired outcomes is 3.
Next, let's determine the total number of possible outcomes. After the first card was drawn, there are only 51 cards left in the deck. So, the total number of possible outcomes is 51.
Now, we can calculate the probability. The probability that both cards drawn are tens, given that the first card was a ten, can be calculated by dividing the number of desired outcomes by the total number of possible outcomes:
Probability = Number of desired outcomes / Total number of possible outcomes
Probability = 3 / 51
Simplifying the fraction, we get:
Probability = 1 / 17
Therefore, the probability that both cards drawn are tens, if the first card was a ten, is 1/17 or approximately 0.0588 (rounded to four decimal places).