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

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