Question

Suppose that you have 11 cards. 5 are green and 6 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 6 yellow cards are numbered 1, 2, 3, 4, 5, and 6. The cards are well shuffled. You randomly draw one card.
• G = card drawn is green
• Y = card drawn is yellow
• E = card drawn is even-numbered

a. List the sample space.
b. Enter probability P(G) as a fraction
c. P(G/E)
d. P(G AND E)
e. P(G or E)
f. Are G and E are mutually exclusive

Answer 1

Answer:

a. S={G1,G2,G3,G4,G5,Y1,Y2,Y3,Y4,Y5,Y6}

b. P(G)=5/11

c. P(G/E)=2/5 or 0.4

d. P(G and E)=2/11 or 0.1818

e. P(G or E)=8/11 or 0.7273

f. G and E not mutually exclusive

Step-by-step explanation:

G={G1,G2,G3,G4,G5}

n(G)=5

Y={Y1,Y2,Y3,Y4,Y5,Y6}

n(Y)=6

E={G2,G4,Y2,Y4,Y6}

n(E)=5

a)

The possible outcomes in sample space are

S={G1,G2,G3,G4,G5,Y1,Y2,Y3,Y4,Y5,Y6}

b)

P(G)=n(G)/n(S)=5/11

c)

P(G/E)=P(G and E)/P(E)

G and E={G2,G4}

n(G and E)=2

P(G and E)=n(G and E)/n(S)=2/11

P(E)=n(E)/n(S)=5/11

P(G/E)=2/5

d)

G and E={G2,G4}

n(G and E)=2

P(G and E)=n(G and E)/n(S)=2/11

e)

P(G or E)= P(G)+P(E)-P(G and E)

P(G or E)=5/11+5/11-2/11

P(G or E)=8/11

f)

G and E are not mutually exclusive because G and E have 2 outcomes in common.

G and E={G2,G4}

Thus, P(G and E)≠0 and G and E are not mutually exclusive events