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wlad13 [49]
3 years ago
15

Michelle draws a card from a standard deck of 52 cards. She replaces the card and draws a second card. What is the probability t

hat she draws a heart and then a spade? [Note: There are 13 each of hearts, spades, clubs, and diamonds.]
Mathematics
2 answers:
erma4kov [3.2K]3 years ago
4 0
To draw a heart, one would be choosing 1 card of 13 possible hearts, and 0 from the remaining 39 non-hearts. With respect to the entire deck, one would be choosing 1 card from 52 total cards. So the probability of drawing a heart is

\dfrac{\dbinom{13}1\cdot\dbinom{39}0}{\dbinom{52}1}=\dfrac{13\cdot1}{52}=\dfrac14

When Michelle replaces the card, the deck returns the normal, so the probability of drawing any card from a given suit is the same, \dfrac14. In other words, drawing a spade is independent of having drawn the heart first.

So the probability of drawing a heart, replacing it, then drawing a spade is \dfrac14\cdot\dfrac14=\dfrac1{16}.
Anit [1.1K]3 years ago
4 0

Answer:

1/16

Step-by-step explanation:

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