Suppose that two cards are randomly selected from a standard? 52-card deck.? (a) what is the probability that the first card is a clubclub and the second card is a clubclub if the sampling is done without? replacement?? (b) what is the probability that the first card is a clubclub and the second card is a clubclub if the sampling is done with? replacement?? (a) if the sampling is done without? replacement, the probability that the first card is a clubclub and the second card is a clubclub is nothing.? (round to three decimal places as? needed.)

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Mathematics

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Suppose that two cards are randomly selected from a standard? 52-card deck.? (a) what is the probability that the first card is a clubclub and the second card is a clubclub if the sampling is done without? replacement?? (b) what is the probability that the first card is a clubclub and the second card is a clubclub if the sampling is done with? replacement?? (a) if the sampling is done without? replacement, the probability that the first card is a clubclub and the second card is a clubclub is nothing.? (round to three decimal places as? needed.)

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Shane Roberson · Answer 1

We can find the answer by using the formula:

Probability = Number of successful events / Number of total events

In this case, the probability of 2 events to be successful is:

Total probability = Probability 1 * Probability 2

A. 1st case

We know that there are 10 clubs in a card, therefore:

Total probability = (10/52) * (9/51)

Total probability = 0.0339 = 3.40%

B. 2nd case

Replacement of the drawn card is made, therefore:

Total probability = (10/52) * (10/52)

Total probability = 0.03698 = 3.70%