Question

A box contains three cards. one card is red on both sides, one card is green on both sides, and one card is red on one side and green on the other. if a student selects one card at random, but only looks at one side of the card – she sees that it is green. what is the chance that the other side is green?
a.2/3
b.3/2
c.1/2
d.1/3

Answer 1

P(G2∣G1)=P(G1∩G2)P(G1)P(G2∣G1)=P(G1∩G2)P(G1)

Exactly one of the three cards has two green sides, so P(G1∩G2)=1/3P(G1∩G2)=1/3. Exactly three of the six sides that could be seen initially are green, so P(G1)=1/2P(G1)=1/2. Thus

P(G2∣G1)=1/31/2=2/3.

Answer: A. 2/3