Suppose that you have 8 cards. 5 are green and 3 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 3 yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card.
G = card drawn is green
E = card drawn is even-numbered
a. List the sample space.
b. P (G) =
c. P (G | E) =
d. P (G AND E) =
e. P (G OR E) =
f. Are G and E mutually exclusive? Justify your answer numerically.
Exercise 2
Refer to the previous problem. Suppose that this time you randomly draw two cards, one at a time, and with replacement.
G1 = first card is green
G2 = second card is green
a. Draw a tree diagram of the situation.
b. P (G1 AND G2) =
c. P (at least one green) =
d. P (G2 | G1) =
e. Are G2 and G1 independent events? Explain why or why not.
Exercise 3
Refer to the previous problems. Suppose that this time you randomly draw two cards, one at a time, and without replacement.
G1= first card is green
G2= second card is green
a. Draw a tree diagram of the situation.
b. P (G1 AND G2) =
c. P(at least one green) =
d. P (G2 | G1) =