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A three digits number was chosen at rand...

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)`

Text Solution

Verified by Experts

The correct Answer is:
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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