Question 911584: Consider selecting one card at a time without replacement from a 52-card deck. Let event A be the first card is a heart, and event B be the second card is a heart
1. What is the probability that the first card is a heart and the second card is also a heart(express in the simplest fraction form)
2. What is the probability that the second card is a heart, given that the first card is a heart (express the answer in simplest fraction form)
3. Are A and B independent? Why or Why not?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Consider selecting one card at a time without replacement from a 52-card deck. Let event A be the first card is a heart, and event B be the second card is a heart
1. What is the probability that the first card is a heart and the second card is also a heart(express in the simplest fraction form)
Ans:: (4/52)(3/51) or 4C2/52C2 = 0.0045
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2. What is the probability that the second card is a heart, given that the first card is a heart (express the answer in simplest fraction form)
P(heart | heart) = P(heart and heart)/P(heart) = 52C2/52C4 = 0.0049
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3. Are A and B independent? Why or Why not?
Ans: no, because P(heart and heart) is not equal to P(heart | heart)
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Cheers,
Stan H.
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