Question

Suppose that you have 9 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacement. Round your answers to four decimal places. G1 = the first card drawn is green G2 = the second card drawn is green

a. P(G1 and G2) =

b. P(At least 1 green) =

c. P(G2|G1) =

d. Are G1 and G2 independent?

They are independent events

They are dependent events

Answer 1

Total number of cards: 9+5 = 14

Out of 14 cards, 9 cards are green. Since draws are done with replacement so probability of getting green card remain same each time. The probability of getting green card in first draw is

P(G1) = 9/14

And likewise

P(G2 | G1) = 9/14

(a)

P(G1 and G2) = P(G2 | G1) * P(G1) = (9/14) * (9/14) = 81 / 196 = 0.4133

(b)

The probability no card is green is

P(no green) = (5/14) * (5/14) = 25 /196

So the probability that at least 1 green is

P(at least 1 green) = 1 - P(no green) = 1 - 25/196 = 171 /196 = 0.8724

(c)

P(G2 | G1) = 9/14

(d)

Yes they are independent because draws are with replacement.