Question

Suppose that you have 8 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards without replacement. 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

Suppose that you have 8 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards without replacement. G1 = the first card drawn is green G2 = the second card drawn is green

Total 13 cards

P(G1)= 8/13

P(G2)= 7/12

a).P(G1 and G2) = (8/13)*(7/12)

=0.358974

b).P(At least 1 green) = P(GY)+P(YG)+P(GG)

=(8/13)*(5/12)+ (5/13)*(8/12)+ (8/13)*(7/12)

=0.871795

c).P(G2|G1) = 7/12

=0.5833

d).Are G1 and G2 independent?

They are dependent events

( probability of occurrence of G1 affects probability of occurrence of G2)