Suppose that you have 9 cards. 4 are red and 5 are purple. The cards are well shuffled. You randomly draw two cards without replacement.

• R1 = first card drawn is red

• R2 = second card drawn is red

P (R1 AND R2) = Round your answer to two decimal places.

P (At least one red) = Round your answer to two decimal places.

P (R2|R1) = Round your answer to two decimal places.

Are R1 and R2 independent?

Answer: P (R1 AND R2) 1/6 = 0.17

P (At least one red) = 5/6=0.83

R2/R1=1/6=0.84

Are R1 $ R2 independent? No

Step-by-step explanation: as card drawn was not replaced, when R1 was drawn, total no of cards reduced to 8, and number of red reduced to 3

A) 4/9*3/8

=1/6 = 0.17

B) The probability of at least one green is

P (at least one green) = 1 - P (no green)

P (no green) = 4/9*3/8 = 12/72 = 1/6

Thus P (at least one green) = 1 - 1/6 = 5/6 = 0.83

C) R2/R1 = 3/8:4/9

=0.84

D) R1 and R2 are not independent because the cards are not replaced.