On one page of a telephone directory , there were 200 telephone numbers . The frequency distribution of their unit's digits is given in the following table :

Out of the numbers on the page , a number is chosen at random .
What is the probability that the unit's digit of the chosen number is
(i) 6 ? `" " ` (ii) a non zero multiple of 3 ?
(iii) a nonzero even number ? `" "` (iv) an odd number ?

Explanation

Number of all telephone numbers on the given page = 200 .
(i) Let `E_(1)` be the event of choosing a number with unit's digit 6 . Number of such numbers = 14.
`therefore` P(getting a number with unit's digit 6)
= `P(E_(1))`
= `("number of times 6 appears as unit's digit")/("total number of numbers on the given page")`
`= (14)/(200) = (7)/(100) = 0.07`.
(ii) Let `E_(2)` be the event of choosing a number whose unit's digit is a nonzero ,multiple of 3 .
Each such number has unit's digit 3 , 6 or 9 .
`therefore` P (getting a number whose unit's digit is a nonzero multiple of 3)
`= P(E_(2))`
`= ("number of numbers with unit's digits 3 , 6 or 9")/("total number of numbers on the given page")`
`= (22 + 14 + 20)/(200) = (56)/(200) = 0.28`.
(iii) Let `E_(3)` be the event of choosing a number whose unit's digit is a nonzero even number .
Each such number has unit's digits 2 , 4 , 6 or 8 .
`therefore` P (getting a number whose unit's digit is a nonzero even number)
` = P(E_(3))`
= `("number of numbers with unit's digit 2 , 4 , 6 or 8")/("total number of numbers on the given page")`
`(22 + 20 + 14 + 16)/(200) = (72)/(200) = (36)/(100) = 0.36`.
(iv) Let `E_(4)` be the event of choosing an odd number .
Each such number has unit's digits 1 , 3 , 5 , 7 or 9 .
`therefore` P (getting a number whose unit's digit is an odd numbers)
= `P(E_(4))`
`= ("number of numbers with unit's digits 1, 3, 5, 7 or 9")/("total number of numbers on the given page")`
`= ((26 + 22 + 10 + 28+ 20))/(200) = (106)/(200) = (53)/(100) = 0.53.`