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Two integers xa n dy are chosen with ...

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.`

Text Solution

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Since x and y each can take values from 0 to 10, so the total number of ways of selecting x and y is `11 xx 11 = 121`. Now, `|x - y| gt 5`
implies `x - y lt -5 or x - y gt 5`
When `x - y gt 5`, we have following cases:
`{:("Values of x","Value of y","Number of cases"),(6,0,1),(7,"0, 1",2),(8,"0, 1, 2",3),(9,"0, 1, 2, 3",4),(10,"0, 1, 2, 3, 4",5),(,"Total number of cases",15):}`
Similarly, we have 15 cases for `x - y lt -5`. There are 30 pairs of values of x and y satisfying these two inequalities. So, favorable number of ways is 30. Hence, required probability is `30//121`.
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