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.

- Rolling a single die, what is the probability of rolling an even number?
- Rolling a single die, what is the probability of rolling a 5?
- Rolling a single die, what is the probability of rolling a 7?
- Rolling a single die, what is the probability of rolling a number less than 4?
- When rolling a pair of dice, what is the probability of rolling the same number on both dice?
- When rolling a pair of dice, what is the probability of rolling a sum of 5?
- When rolling a pair of dice, what is the probability of rolling a sum of 12?
- When rolling a pair of dice, what is the probability of rolling a sum of 2?
- When rolling a pair of dice, what is the probability of rolling a sum less than 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-

_______________________________________________

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-

A
standard pair of 6 sided dice is rolled. What is the probability of
rolling a sum less than or equal to 6?

A standard pair of six-sided dice is rolled. What is the
probability of rolling a sum less than or equal to 7? Express your
answer as a fraction or a decimal number rounded to four decimal
places.

please answer the following questions:
*An experiment consists of rolling two dice. Find the
probability that the sum is greater than or equal to 9 or
even.
*A die is rolled. find
a- sample space for the experiment.
b- event of rolling an even number.
c- probability of rolling at least a number 3.

An experiment consists of rolling two 6-sided dice. Find the
probability that the sum of the dice is at most 5. Write your
answer as a simplified fraction, i.e. a/b

You have one six-sided dice and one ten-sided dice. What is the
probability of rolling:
a. both dice even
b. a sum greater than 12
c. a sum equal to 10
d. an odd sum

A standard pair of six-sided dice is rolled. What is the
probability of rolling a sum less than 3? Express your answer as a
fraction or a decimal number rounded to four decimal places.

A standard pair of six-sided dice is rolled. What is the
probability of rolling a sum less than 10? Express your answer as a
fraction or a decimal number rounded to four decimal places.

Imagine rolling two fair 6 sided dice. What is the probability
the number rolled on the first die is even or the sum of the rolls
is 10?

You roll a six-sided die. Find the probability of each of the
following scenarios.
(a) Rolling a 6 or a number greater than 3
(b) Rolling a number less than 5 or an even number
(c) Rolling a 4 or an odd number

A standard pair of six sided dice is rolled. what is the
probability of rolling a sum greater than 2?

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