Question

For the following questions, find the probability using a standard 6-sided die or two 6-sided dice. Write your answer as a fraction or with a colon in lowest terms.

1. Rolling a single die, what is the probability of rolling an even number?
2. Rolling a single die, what is the probability of rolling a 5?
3. Rolling a single die, what is the probability of rolling a 7?
4. Rolling a single die, what is the probability of rolling a number less than 4?
5. When rolling a pair of dice, what is the probability of rolling the same number on both dice?
6. When rolling a pair of dice, what is the probability of rolling a sum of 5?
7. When rolling a pair of dice, what is the probability of rolling a sum of 12?
8. When rolling a pair of dice, what is the probability of rolling a sum of 2?
9. When rolling a pair of dice, what is the probability of rolling a sum less than 10?
10. When rolling a pair of dice, what is the probability of rolling a sum greater than or equal to 6?

Answer 1

The sample space associated with the random experiment of rolling a single die is:

So, there are 6 elements in the sample space S. And the, Total number of elementary events =6

(a) Probability of rolling an even number: An even number is obtained, if we obtain any one of 2, 4, 6 as an outcome.

So, the favourable number of elementary events =3

Hence,

(b) Probability of rolling a 5: When a single die is thrown , then the probability of getting any one out of 6 outcome is ,

Hence, the probability of rolling a 5 is-

(c) Probability of rolling 7: The sample space for rolling a single die is

Since, 7 is not in the sample space, so the probability of rolling 7 is 0.

(d) Probability of rolling a number less than 4: In a sample space a number less than 4 are {1, 2, 3}

So, the probability of rolling a number less than 4 is-

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When a two 6-sided dice are thrown together the sample space S associated with the random experiment is given by-

So, Total number of elementary events=36

(e) Probability of rolling the same number on both dice: The same number on both dice means when we see the outcome as and these are total number of 6 elementary events.

So, the probability of rolling the same number on both dice is-

(f) Probability of rolling a sum of 5: We get the sum of 5 when the following outcome has occurred

So, the probability of rolling a sum of 5 is-

(g) Probability of rolling a sum of 12: We get the sum of 12 when the following outcome has occurred , i.e.,

So, the probability of rolling a sum of 12 is-

(h) Probability of rolling a sum of 2: We get the sum of 2 when, the following outcome has occurred, i.e.,

So, the probability of rolling a sum of 2 is-

(i) Probability of rolling a sum less than 10: We get the sum less than 10, when the following outcome has occurred, i.e.,

So, there are Total number of favourable outcomes are 30

(j) Probability of rolling a sum greater than or equal to 6: We get the sum greater than or equal to 6, when the following outcome has occurred, i.e.,

So, the Total number of favourable outcomes are 26

So, the probability of rolling a sum greater than or equal to 6 is-