Question

Suppose that you have 7 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?

Answer 1

Answer:

a. 7/22

b. 28/33

c. 7/22

d. dependent events

Step-by-step explanation:

The total number of cards is given as 7 + 5 = 12.

The probability if a card being green on the first pick, P(G) =  7/12

The probability of a card being yellow on the first pick, P(Y) = 5/12

Because there is no replacement, the card are going to be short by one card. Therefore, the second pick will be like this:

P(GG)  = ( 7/12×6/11)

P(GY) = ( 7/12 × 5/11)

P(YG) = ( 5/12×7/11)

P(RR) = ( 5/12 ×4/11)

a. P (G1 and G2) = ( 7/12×6/11)

                          = 7/22

b. P( At least one is green) = ( 7/12×6/11) +  ( 7/12 × 5/11) + ( 5/12×7/11)

                           = 28/33

c. P(G2G1)           = 7/22

d. the events are dependent. They do not give the same result.