Probability that number is neither even nor multiple of 3

[Vemuri]

The integers from 1 to 100 inclusive are each written on a single slip of paper and dropped into a jar. If one slip of paper is removed at random, approximately what is the probability that the number on it is neither even nor a multiple of 3?

A. 83%
B. 67%
C. 50%
D. 33%
E. 17%

[Dream Weaver]

IMO D (33%)

My approach could be wrong, so please specify the OA. But, here's how I conclude :

Probability of finding an even number is 50/100
Probability of finding a multiple of 3 is 33/100
Probability of finding an even number which is also a multiple of 3 is 16/100

So, I arrive to the probability of finding a even number or a multiple of 3 to be 50/100 + 33/100 - 16/100 = 67/100

What we need is opposite of this : 1- 67/100 = 33/100

Please specify the OA. Thanks !!

[Vemuri]

Hi Dream Weaver,

Your approach & answer are both correct

[Dream Weaver]

[KICKGMATASS123]

How do u find an even number that is also a multiple of 3 number?

Is there an approach to this?

Thanks in advance

[RBurroughs]

I did this pretty quick in my head.

1/3 are multiples of 3, and 1/2 are even[ (3) odd, (6) even, 9 (odd)...]

so keeping true 1/2 are odd/even, 1/2 of the 66 left are odd, or 33%

[RBurroughs]

How do u find an even number that is also a multiple of 3 number?

Is there an approach to this?

Thanks in advance

1/3 are multiples of 3, 1/2 of these are even.

1/3*1/2 = 1/6