i have some algebra questions about rolling the dice. 1.What is the probability

Question

i have some algebra questions about rolling the dice.

1.What is the probability of getting a total of at most 1 from rolling three dice?

2.What is the probability of getting a total of at most 2 from rolling three dice? .

3.What is the probability of getting a total of at most 3 from rolling three dice? .

4.What is the probability of getting a total of at most 4 from rolling three dice? .

5.What is the probability of getting a total of at most 5 from rolling three dice? .

6.What is the probability of getting a total of at most 6 from rolling three dice? .

Note: your answers should be entered as exact rational numbers.

Explanation / Answer

(1). When three dice are rolled, total number of outcomes are 6^3 = 216

Number of events of getting a total of atmost 1 = 0

Hence, probability = 0 / 216 = 0

(2). Number of events of getting a total of atmost 2 = 0

Hence, probability = 0 / 216 = 0

(3). Number of events of getting a total of atmost 3 = 1

i.e., (1,1,1)

Hence, probability = 1 / 216

(4). Number of events of getting a total of atmost 4 = 4

i.e., (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1)

Hence, probability = 4 / 216 = 1/ 54

(5). Number of events of getting a total of atmost 5 = 10

i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1) and (1, 2, 2).

Hence, probability = 10 / 216 = 5 / 108

(6). Number of events of getting a total of atmost 6 = 20

i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1), (1, 2, 2), (1, 1, 4), (1, 4, 1), (4, 1, 1), (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1) and (2, 2, 2).

Hence, probability = 20 / 216 = 5 / 54

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