1- (a) What is the probability of rolling a pair of dice and obtaining a total s

Question

1- (a) What is the probability of rolling a pair of dice and obtaining a total score of

9 or more? (b) What is the probability of rolling a pair of dice and obtaining a

total score of 7?

2- A box contains four black pieces of cloth, two striped pieces, and six dotted pieces. A piece is selected randomly and then placed back in the box. A second piece is selected randomly. What is the probability that: a. both pieces are dotted? b. the first piece is black and the second piece is dotted? c. One piece is black and one piece is striped?

3- A card is drawn at random from a deck. (a) What is the probability that it is an ace or a king? (b) What is the probability that it is either a red card or a black card?

Explanation / Answer

1a)

Total number of outcomes for a event of roll of two dice = 6*6 = 36

the probability of rolling a pair of dice and obtaining a total score of 9 or more =

for total score 9 = (3,6)(4,5)(5,4)(6,3)

for total score 10 = (4,6)(5,5)(6,4)

for total score 11 = (5,6)(6,5)

= 9/36

b)

for sum be 7

= (1,6)(2,5)(3,4)(4,3)(5,2)(6,1)

= 6/36 = 1/6

2 a) 4 black , 2 striped , 6 dotted Total = 12

probability of both pieces to be dotted = 6/12 * 6/12 = 1/4 = 0.25

b)

probability the first piece is black and the second piece is dotted = 4/12 * 6/12 = 1/6

c) probability that One piece is black and one piece is striped = 4/12 * 2/12 = 1/18

3

a) the probability that it is an ace or a king = 8/52

b) probability that it is either a red card or a black card = 52/52 = 1

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