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Statistics Club Cards Questions

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1) What is the probability that the first card is a club and the second card is a club if the sampling is
done without replacement?
We know that there are 13 cards that are a club in a standard 52-card deck. So, the probability that
the first card is a club is 13/52 = 0.25.
Then, since the sampling is done without replacement, the probability that the second card is a club
is 12/51 = 0.235294.
Finally, the probability than probability that the first card is a club and the second card is a club if
the sampling is done without replacement is 0.25 * 0.235294 = 0.058824
2) What is the probability that the first card is a club and the second card is a club if the sampling is
done with replacement?
The difference between this exercise and the previous one is that the sampling is done with
replacement. Therefore, the probability that the first card is a club is again 13/52 = 0.25. Then, the
probability that the second card is a club is again 13/52 (here is the difference with the first
exercise).
Finally, is the probability that the first card is a club and the second card is a club if the sampling is
done with replacement is 0.25 * 0.25 = 0.0625
3) What is the probability that the first card is a club and the second card is a heart if the sampling is
done without replacement?
The probability that the first card is a club is 13/52 = 0.25. Then, we know that there are 13 hearts
and there are 51 cards left (because the sampling is done without replacement). Therefore, the
probability that the second card is a heart is 13 / 51 = 0.254902.
Finally, the probability that the first card is a club and the second card is a heart if the sampling is
done without replacement is 0.25 * 0.254902 = 0.063725
4) What is the probability that the first card is a club and the second card is a heart if the sampling is
done with replacement?
The probability that the first card is a club is 13/52 = 0.25. Then, we know that there are 13 hearts
and there are again 52 cards (because the sampling is done with replacement). So, the probability
that the second card is a heart is 13/52 = 0.25.
Finally, the probability that the first card is a club and the second card is a heart if the sampling is
done with replacement is 0.25 * 0.25 = 0.0625

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1) What is the probability that the first card is a club and the second card is a club if the sampling is done without replacement? We know that there are 13 cards that are a club in a standard 52-card deck. So, the probability that the first card is a club is 13/52 = 0.25. Then, since the sampling ...
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