— Save \& Exit Certify Lesson: 4.3 Multiplication Rules for Probab...
SIERRA SCOTT
Question 3 of 14, Step 1 of 1
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Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a heart and then, without replacement, a spade? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer
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Step 1 ：The problem is asking for the probability of drawing a heart and then a spade from a deck of 52 cards without replacement.

Step 2 ：A standard deck of 52 cards contains 13 cards of each suit: hearts, diamonds, clubs, and spades.

Step 3 ：The probability of drawing a heart from the deck on the first draw is \(\frac{13}{52}\) or \(\frac{1}{4}\).

Step 4 ：After drawing a heart, there are now 51 cards left in the deck. The probability of drawing a spade from the remaining cards is \(\frac{13}{51}\).

Step 5 ：The probability of both events happening is the product of their individual probabilities.

Step 6 ：So, the probability of drawing a heart and then a spade is \(\frac{1}{4} \times \frac{13}{51}\).

Step 7 ：Calculating this gives us a probability of approximately 0.0637.

Step 8 ：Final Answer: The probability of drawing a heart and then a spade from a deck of 52 cards without replacement is \(\boxed{0.0637}\).