Suppose you have 6 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacement.

Question

G₁ = The first card drawn is green

G₂ = The second card drawn is green

a. Calculate P(G1 and G2)

b. Calculate P(at least one green)

c. Calculate P(G2 | G1)

Answer 1

a

P(G1 and G2) = P(G1) * P(G2|G1)

P(G1) = 6/11

P(G2|G1) = 5/10 = 1/2

so P(G1 and G2) = 6/11 * 1/2 = 3/11

b

at least one green = 1 - probability no green

probability no green = 5/11 * 4/10 = 20/110 = 2/11

so probability at least 1 green = 1 - 2/11 = 9/11

c

P(G2 | G1) = 1/2 from above