Two dice- one blue and one grey- are thrown at the same time-i Write down all the possible outcomes and complete the following table-Event- Sum of two dice 2 3 4 5 6 7 8 9 10 11 12 Probability 1-36 5-36 1-36 ii A student argues that -there are 11 possible outcomes 2-3-4-5-6-7-8-9-10-11 and 12 - Therefore- each of them has a probability 1-11 - Do you agreewith this argument-

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Standard X

Mathematics

Introduction to Probability

Two dice, one...

Question

Two dice, one blue and one grey, are thrown at the same time.

(i) Write down all the possible outcomes and complete the following table:

Event:

Sum of two dice

2

3

4

5

6

7

8

9

10

11

12

Probability

(ii) A student argues that ‘there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability. Do you agree with this argument?

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Solution

(i) It can be observed that,

To get the sum as 2, possible outcomes = (1, 1)

To get the sum as 3, possible outcomes = (2, 1) and (1, 2)

To get the sum as 4, possible outcomes = (3, 1), (1, 3), (2, 2)

To get the sum as 5, possible outcomes = (4, 1), (1, 4), (2, 3), (3, 2)

To get the sum as 6, possible outcomes = (5, 1), (1, 5), (2, 4), (4, 2),

(3, 3)

To get the sum as 7, possible outcomes = (6, 1), (1, 6), (2, 5), (5, 2),

(3, 4), (4, 3)

To get the sum as 8, possible outcomes = (6, 2), (2, 6), (3, 5), (5, 3),

(4, 4)

To get the sum as 9, possible outcomes = (3, 6), (6, 3), (4, 5), (5, 4)

To get the sum as 10, possible outcomes = (4, 6), (6, 4), (5, 5)

To get the sum as 11, possible outcomes = (5, 6), (6, 5)

To get the sum as 12, possible outcomes = (6, 6)

Event:

Sum of two dice

2

3

4

5

6

7

8

9

10

11

12

Probability

(ii)Probability of each of these sums will not be as these sums are not equally likely.

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Similar questions

Q. Two dice, one blue and one grey, are thrown at the same time. Complete the following table:

Event: 'Sum on two dice'	2	3	4	5	6	7	8	9	10	11	12
Probability

From the above table a student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability

\frac{1}{11} .

Do you agree with this argument?

Q. (i) Complete the following table:

Event: 'Sum on $2$ dice'	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$
Probability	$\frac{1}{36}$						$\frac{5}{36}$				$\frac{1}{36}$

(ii) A student argues that there are

11

possible outcomes

2, 3, 4, 5, 6, 7, 8, 9, 10, 11

and

12

. Therefore, each of them has a probability

\frac{1}{11}

. Do you agree with this argument?
Justify your answer.

Q. Two dice, one blue and one grey are thrown at the same time. Complete the following table:

Event: Sum on two dice'	2	3	4	5	6	7	8	9	10	11	12
Probability

From the above table a student argues that there are

11

possible outcomes

2, 3, 4, 5, 6, 7, 8, 9, 10, 11

and

12

. Therefore, each of them has a probability of

\frac{1}{11}

. Do you agree with this argument?

A student argues that there are

11

possible outcomes (sum of numbers on both dice)

2, 3, 4, 5, 6, 7, 8, 9, 10, 11

and

12

when we throws two dice simultaneously. Therefore each of them has a probability

\frac{1}{11} .

Do you agree with this argument? Justify your answer.

(i) Complete the following table:

$\begin{matrix} Event:'Sum of 2 dice' & Probability 2 & \frac{1}{36} 34567 8 & \frac{5}{36} 91011 12 & \frac{1}{36} \end{matrix}$

(ii) A student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability $\frac{1}{11}$ . Do you agree with this argument? Justify your answer.

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