Problem
4. From a deck of cards, use only the hearts to answer the following questions. Shuffle the hearts and draw from them face down. a) What is the probability of drawing the six of hearts? Give your answer as a fraction, a decimal, and a percent. b) What is the probability of drawing a face card? Give your answer as a fraction, a decimal, and a percent. c) What is the probability of drawing the ace of hearts? d) Suppose you drew a card that was not the ace, kept it out of the pile, and drew another card. What would be the probability of getting an ace in the second draw? Give your answer as a percent.
Solution
Step 1 ：a) The probability of drawing the six of hearts is \(\frac{1}{13}\), which is approximately \(0.0769\) or \(7.69\%\).
Step 2 ：b) The probability of drawing a face card is \(\frac{3}{13}\), which is approximately \(0.2308\) or \(23.08\%\).
Step 3 ：c) The probability of drawing the ace of hearts is \(\frac{1}{13}\), which is approximately \(0.0769\) or \(7.69\%\).
Step 4 ：d) The probability of getting an ace in the second draw after drawing a non-ace card is \(\frac{1}{12}\), which is approximately \(0.0833\) or \(8.33\%\).
