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State true or false.

Two dice are rolled simultaneously.

Consider the following 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 $= 111$ .

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True

False

answer is B.

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Detailed Solution

It is given a data,
Question Image

The probability of an event E is given as-

P (E) = N u m b e r o f o u t c o m e s f a v o u r a b l e t o E N u m b e r o f a l l p o s s i b l e o u t c o m e s o f t h e e x p e r i m e n t

Given that the two dice are rolled simultaneously.
Therefore, the total number of outcomes

= 6 × 6 = 36

Now, the possible outcomes to get the sum of 2

= (1, 1)

∴ P (2) = 136

Possible outcomes to get the sum of 3

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

∴ P (3) = 236 = 118

Possible outcomes to get the sum of 4

= (3, 1), (1,3), (2,2)

∴ P (4) = 336

Possible outcomes to get the sum of 5

= (4, 1), (1,4), (2,3), (3,2)

∴ P (5) = 436 = 19

Possible outcomes to get the sum of 6

= (5, 1), (1,5), (2,4), (4,2), (3,3)

∴ P (6) = 536

Possible outcomes to get the sum of 7

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

∴ P (7) = 636 = 16

Possible outcomes to get the sum of 8

= (6, 2), (2,6), (3,5), (5,3), (4,4)

∴ P (8) = 536

Possible outcomes to get the sum of 9

= (6, 3), (3,6), (5,4), (4,5)

∴ P (9) = 436 = 19

Possible outcomes to get the sum of 10

= (6, 4), (4,6), (5,5)

∴ P (10) = 336

Possible outcomes to get the sum of 11

= (6,5), (5,6)

∴ P (11) = 236 = 118

Possible outcomes to get the sum of 12

= (6, 6)

∴ P (12) = 136

Since, none of the above 11 possible outcomes has a probability =

111

.
Hence, the given argument is false.
Hence option (2) is false.

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