(a) What is the probability that the first card is a king and the second card is

Question

(a) 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? (b) 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? (a) If the sampling is done without replacement, the probablity that the first card is a king and the second card is a king is(Round to three decimal places as needed.) (b) 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.) 2 6 8 0 3

Explanation / Answer

a)
There are 4 kings in a standard 52-card deck.
The probability to choose first card as king = 4 / 52 = 1/13
If the sampling is done without replacement, now 3 kings remain in 51 cards.
The probability to choose second card as king = 3 / 51 = 1/17

The probability to choose first card as king and second card as king if the sampling is done without replacement
= (1/13) * (1/17) = 0.005

b)

If the sampling is done with replacement, then 4 kings will exist in 52 cards.
The probability to choose second card as king = 4 / 52 = 1/13

The probability to choose first card as king and second card as king if the sampling is done without replacement
= (1/13) * (1/13) = 0.006

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