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A three digits number was chosen at random. Find the probability that it is divisible by both 2 and 3.A. `(1)/(12)`B. `(1)/(6)`C. `(1)/(9)`D. `(1)/(8)`

Answer» Correct Answer - B
Let the number be `x,100lexle999`.
A number divisible by both 2 and 3 must be divisible by the LCM of (2, 3)=6.
Least value of x divisible by 6=102=6(17)
Greatest value of x divisible by 6=996=6(166)
There are 150 values of x divisible by 6.
Required probability `=(150)/(900)=(1)/(6)` (There are 900 three digits numbers).


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