Question

When we roll a pair of dice, what are the probabilities of getting: (Hint: Determine the sample space: how many possible outcomes can you have when rolling two dice?)

a.) 9

b.) 11

c.) 9 or 11

d.) 7

e.) 9 or 7

f.) 9,11, or 7

Answer 1

Total number of possible combinations of outcomes of the two die

= 6 * 6 = 36

a) For an outcome of 9, the possible combinations are

(3,6) , (4,5), (6,3) and (5,4)

Hence, the probability of getting 9

= 4/36 = 1/9

b) For an outcome of 11, the possible combinations are

(5,6) and (6,5)

Hence, the probability of getting 11

= 2/36 = 1/18

c) Probability of getting 9 or 11

= Probability of getting 9 + Probability of getting 11

= 1/9 + 1/18 = 1/6

d) For an outcome of 7, the possible combinations are

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

Hence, the probability of getting 7

= 6/36 = 1/6

e) Probability of getting 9 or 7

= Probability of getting 9 + Probability of getting 7

= 1/9 + 1/6 = 5/18

f) Probability of getting 9 , 11 or 7

= Probability of getting 9 + Probability of getting 11 + Probability of getting 7

= 1/9 + 1/18 + 1/6 = 1/3

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