Question

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?

Answer 1

(a) without replacement:
P(S)=13/52=1/4
P(SS)=(1/4)*(12/51)=1/17
Probability of selecting two spades without replacement is 1/17.

(b) with replacement
P(S)=13/52=1/4
P(SS)=(1/4)(13/52)=1/16
Probability of selecting two spades with replacement is 1/16.

Answer 2

(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 = $\frac{number\ of\ favorable\ outcomes}{Total\ number\ of\ cases}$

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

For fist card = $\frac{13}{52}$

for the second card = $\frac{12}{51}$ (because no replacement)

then collective Probability =$\frac{13}{52}$ × $\frac{12}{51}$

= 1/17 or 0.05882

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

For fist card = $\frac{13}{52}$

for the second card = $\frac{13}{52}$ (with replacement)

then collective Probability = $\frac{13}{52}$ × $\frac{13}{52}$

= 1/16 or 0.0625.

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