Suppose that two cards are randomly selected from a standard 52-card deck What i

Question

Suppose that two cards are randomly selected from a standard 52-card deck What is the probability that the first card is a king and the second card is a king if the sampling is done without replacement? What is the probability that the first card is a king and the second card is a king if the sampling is done with replacement? If the sampling is done without replacement, the probability that the first card is a king and the second card is a king is (Round to three decimal places as needed) If the sampling is done with replacement, the probability that the first card is a king and the second card is a king is (Round to three decimal places as needed)

Explanation / Answer

a)

Probability of first card being a king is: 4/52=1/13

Now three kings are left in 51 cards so probability of second card being a king is:3/51=1/17

Hence the probability is: (1/13)*(1/17)=1/221

b)

Probability of first card being a king is :4/52=1/13~0.005

Since second card is chosen after replacement so

probability of second card is a king is:4/52=1/13

So probability=(1/13)*(1/13)=1/169~0.006

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