Suppose that two cards are randomly selected from a standard 52-card deck. (a) what is the probability that the first card is a spadespade and the second card is a spadespade if the sampling is done without replacement? (b) what is the probability that the first card is a spadespade and the second card is a spadespade if the sampling is done with replacement?

(a) The probability that the first card is a spade and the second card is a spade if the sampling is done without replacement - 1/17 or 0.05882

(b) The probability that the first card is a spade and the second card is a spade if the sampling is done with replacement- 1/16 0r 0.0625

Given:

two cards are drawn are randomly selected from a standard 52- cards deck.

then,

Total cards=52

Total number of spade cards=13

Formula: Probability =

A. The probability of drawing 2 cards of spade without replacement:

For fist card =

for the second card = (because no replacement)

then collective Probability = ×

= 1/17 or 0.05882

B. The probability of drawing 2 cards of spade with replacement:

For fist card =

for the second card = (with replacement)

then collective Probability = ×

= 1/16 or 0.0625.

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