Question

Suppose that you have 9 cards. 6 are green and 3 are yellow. The 6 green cards are numbered 1, 2, 3, 4, 5, and 6. 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

• Y = card drawn is yellow •

E = card drawn is even-numbered

a. List the sample space. (Type your answer using letter/number combinations separated by commas. Example: G1, Y1, ...)

b. Enter the probability as a fraction.

P(G) =

c. Enter the probability as a fraction.

P(G | E) =

d. Enter the probability as a fraction.

P(G AND E) =

e. Enter the probability as a fraction.

P(G OR E) =

f. Are G and E mutually exclusive?

Yes

No    

Answer 1

a) Sample space = {G1, G2, G3 , G4 , G5 , G6 , Y1, Y2, Y3 }

b) P(G) = 6/9 = 2/3

c) P(G/ E) = P(G E) / P(E)

E = even cards = { G2, G4 , G6 , Y2,}

    P(G E) = 3/9

P(E) = 4 / 9

   P(G/ E) = P(G E) / P(E) = (3/9) / (4/9) = 3/4

d) P(G and E) =  P(G E) = 3/9 = 1/3

e) P(G or E) = P(G) + P(E) - P(G E) = 6/9 + 4/9 - 3/9 = 7/9

f) Are G and E mutually exclusive ?

No G and E are not mutually exclusive as P(G E) is not equal to zero

For mutually exclusive events P(G or E) = P(G) + P(E)