CHAPTER 3. PROBABILITY TOPICS Exercise1 Suppose that you have 8 cards. 5 are gre
ID: 3363950 • Letter: C
Question
CHAPTER 3. PROBABILITY TOPICS Exercise1 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 (GIE)- 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 3Explanation / Answer
Exercise 1
Solution:
G = card drawn is green
Y = card drawn is yellow
E = card drawn is even-numbered
a) List sample space
{G1,G2,G3,G4,G5,Y1,Y2,Y3}
b) P(G) :
there are 5 G's out of 8 cards, so probability is 5/8
c) P(G|E) = P(G and E )/P(E) = (2/8)/(3/8) = 2/3
d) P(G AND E)
There are 2 ways, G2 and G4, to have both Green AND Even out of 8 ways, so
the probability P(G AND E) = 2/8 = 1/4
e) P(G or E)
There are 6 ways, G1,G2,G3,G4,G5 or Y2 to have one OR the other of either Green OR Even. So the probability is 6/8 which reduces to 3/4.
f) Think of the word "exclusiVE" as "excludiNG". They do not EXCLUDE each other.
They are not mutually exclusive events because to be mutually exclusive events, the two events must be such that if one of them is true the other MUST BE false. In other words, the truth of one would have to EXCLUDE the other. Here Green does not EXCLUDE Even, because for instance, we could
draw G2.