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.)

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%

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11