Question

You draw 2 cards from a standard deck of cards without replacement. 1) What is the...

You draw 2 cards from a standard deck of cards without replacement.

1) What is the probability that the second card is a queen given that the first card is a jack?

2) What is the probability that the second card is red given that the first card was a heart?

3) What is the probability that the second card is red given that the first card is red?

Math   Statistics-And-Probability   
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Answer #1

a) We need to find the probability that the second card is a queen given that the first card is a jack. Suppose we took a jack card first next there are 51 remaining cards in our hand to pic next queen. Since these are independent and there are 4 queens so the required probability is 4/51

b)To find  the probability that the second card is red given that the first card was a heart . Since heart is red there are only 25 red cards are remaining then the probability is 25/51

c) To find the probability that the second card is red given that the first card is red. There are 25 red cards remaining there if we choose the first red card so the required probability is 25/51

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