Question 1175613
there are 15 odd numbers: 1,3,5,...,29
there are 6 numbers divisible by 5:  5,10,15,20,25,30
there are 3 numbers that are both:   5,15,25<br>

P(odd or number divisible by 5) = 15/30 + 6/30 - 3/30 = 18/30 = {{{highlight( 3/5 ) }}}<br>

If you are wondering why the subtraction, the intersection needs to be subtracted once because it is included in each of the other two probabilities (i.e. it is counted twice).
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A second way to look at it is to find independent sets, then there is no intersection and we can just add things.  We have the 15 odd numbers { 1,3,5,...,29 }  + even numbers divisible by 5: { 10,20,30 }  which makes 18 total results of interest: 18/30 = 3/5, as above.  <br>

The first method is more general (inclusion-exclusion principle) and is far more powerful when there are many overlapping sets.