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Two integers xa n dy are chosen with r...

Two integers `xa n dy` are chosen with replacement out of the set `{0,1,,2,3 ,.....10}dot` Then find the probability that `|x-y|> 5.`

A

`(81)/(121)`

B

`(30)/(121)`

C

`(25)/(121)`

D

`(20)/(121)`

Text Solution

Verified by Experts

The correct Answer is:
B
Since x and y each can take values from 0 to 10. So, the total number of ways of selecting x and y is `11xx11=121`.
Now, `|x,y| gt 5 implies implies x-y lt -5 " or ", x-y gt 5`
There are 30 pairs of values of x and y satisfying these two inequalities,
So, favourable number of elementary events=30.
Hence, required probability `=(30)/(121)`
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