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State true or false.

Two dice are numbered $1, 2, 3, 4, 5, 6$ , and $1, 1, 2, 2, 3, 3$ , respectively. They are thrown and the sum of the numbers on them is noted. The probability of getting each sum from $2$ to $9$ separately will all be equal to $16$ .

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True

False

answer is B.

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Detailed Solution

It is given that, two dice are numbered

1, 2, 3, 4, 5, 6

and

1, 1, 2, 2, 3, 3

.
We have to find the probability of getting each sum from

2

9

separately.
The total number of possible outcome for two dice is

36

The favorable outcome for sum of the number on

2

dice is

2

are

(1, 1)

and (1,1).
The probability for the sum of the number on both dice is

2

is,

P (s u m is 2)= 236

= 118

The favorable outcome for sum of the number on two dice is 3 are

(1, 2), (1, 2), (2, 1), (2, 1)

.
The number of favorable outcome is

4

.
The probability for the sum of the number on both dice is

3

is,

P (s u m is 3)= 436

= 19

The favorable outcome for sum of the number on two dice is

4

are

(2, 2), (2, 2), (3, 1), (3, 1), (1, 3), (1, 3)

.
The number of favorable outcome is

6

.
The probability for the sum of the number on both dice is

4

is,

P (s u m is 4)= 636

= 16

The favorable outcome for sum of the number on two dice is

5

are

(2, 3), (2, 3), (3, 2), (3, 2), (4, 1), (4, 1)

.
The number of favorable outcome is

6

.
The probability for the sum of the number on both dice is

5

is,

P (s u m is 5)= 636

= 16

The favorable outcome for sum of the number on two dice is

6

are

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

.
The number of favorable outcome is

6

.
The probability for the sum of the number on both dice is

6

is,

P (s u m is 6)= 636

= 16

The favorable outcome for sum of the number on two dice is

7

are

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

.
The number of favorable outcome is

6

.
The probability for the sum of the number on both dice is

7

is,

P (s u m is 7)= 636

= 16

The favorable outcome for sum of the number on two dice is

8

are

(6, 2), (6, 2), (5, 3), (5, 3)

.
The number of favorable outcomes is 4 .
The probability for the sum of the number on both dice is

8

is,

P (s u m is 8)= 436

= 19

The favorable outcome for sum of the number on two dice is

9

are

(6, 3), (6, 3)

.
The number of favorable outcome is

2

.
The probability for the sum of the number on both dice is 9 is,

P (s u m is 9)= 236

= 118

Hence the probabilities are:

P (s u m is 2)= 118, P (s u m is 2)= 118, P (s u m is 3)= 19, P (s u m is 4)= 16, P (s u m is 5)= 16, P (s u m is 6)= 16, P (s u m is 7)= 16, P (s u m is 8)= 19, P (s u m is 9)= 118

All the probabilities from

2

9

are not same as

16

, they are different.
Hence, the correct statement is the probability of getting each sum from 2 to 9 separately will all be equal to

\frac{1}{6}

.
Hence, the statement is false.
Therefore, option 2 is correct.

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State true or false.Two dice are numbered 1,2,3,4,5,6 , and 1,1,2,2,3,3 , respectively. They are thrown and the sum of the numbers on them is noted. The probability of getting each sum from 2 to 9 separately will all be equal to 1 6 .

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Detailed Solution

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State true or false.

Two dice are numbered $1, 2, 3, 4, 5, 6$ , and $1, 1, 2, 2, 3, 3$ , respectively. They are thrown and the sum of the numbers on them is noted. The probability of getting each sum from $2$ to $9$ separately will all be equal to $16$ .