If you pull a card and it is a heart, you turn it back and you pull another card. If it is not heart, you pull another card without returning the first card back. What is the probability that the second card is a heart.
Probability of the second heart card
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probability
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0What are your thoughts on the problem? – 2017-01-31
2 Answers
0
Case 1 -
First card is heart = $\frac {13}{52} = \frac {1}{4}$
Second card is heart = $\frac {13}{52} = \frac {1}{4}$
Probability = $\frac {1}{4} × \frac {1}{4} = \frac {1}{16}$
Case 2 -
First card not heart = $\frac {39}{52} = \frac {3}{4}$
Second card is heart = $\frac {13}{51}$
Probability = $\frac {3}{4} × \frac {13}{51} = \frac {13}{68}$
Total probability = $\frac {1}{16} + \frac {13}{68} = \frac {21}{272}$
0
1/4 of the time the second card will have a probability of 1/4 of being hearts (you pull hearts as the first card)
3/4 of the time the second card will have a probability of 13/51 of being hearts (you don't pull hearts as the first card)
Overall probability: (1 * 1/4 + 3 * 13/51)/4 = 0.253676471