Sara draws the 6 of hearts from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card. a. Determine the probability that the second card is another 6 . \[ P(6 \mid 6 \text { of hearts })= \] b. Determine the probability that the second card is another heart. \[ P(\text { heart } \mid 6 \text { of hearts })= \]
Solution
Step 1 ：Sara draws the 6 of hearts from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card.
Step 2 ：We need to determine the probability that the second card is another 6. There are 4 sixes in a deck of 52 cards. Since we've already drawn one, there are now 3 sixes left in a deck of 51 cards. So, the probability is \(\frac{3}{51}\).
Step 3 ：We also need to determine the probability that the second card is another heart. There are 13 hearts in a deck of 52 cards. Since we've already drawn one, there are now 12 hearts left in a deck of 51 cards. So, the probability is \(\frac{12}{51}\).
Step 4 ：Final Answer: a. The probability that the second card is another 6 is \(\boxed{0.0588}\) or \(\boxed{\frac{3}{51}}\). b. The probability that the second card is another heart is \(\boxed{0.2353}\) or \(\boxed{\frac{12}{51}}\).
