A die is thrown twice. What is the probability that 5 will not come up either time?

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1318

518

1136

2536

answer is D.

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Detailed Solution

It is given a die is thrown twice.
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

Now, when a dice is thrown once, there are 6 possible outcomes.
So, when a dice is thrown twice-
Total possible outcomes

= 6 × 6 = 36

Possible outcomes when 5 comes up on either time are

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

Number of favourable outcomes=Total number of cases where 5 comes up at least once

= 11

Substituting the values, we get

P (5 coming up at least once) = 1136

Now, for any event E, we have

P E + P E ¯ = 1

⇒ P E ¯ = 1 − P E

where

stands for ‘not E’
Therefore, the probability of 5 not coming up on either time is-

P 5 not coming up either time = 1 − 1136 = 36 − 11 36 = 2536

Hence,

2536

is the probability of 5 not coming up either time.
So, option (4) is correct.

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