Question 1175613: If you are to pick a number from the box with numbers 1-30, what is the probability that you will pick a number that is odd or is divisible by 5?
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! 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
P(odd or number divisible by 5) = 15/30 + 6/30 - 3/30 = 18/30 = 
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).
---------
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.
The first method is more general (inclusion-exclusion principle) and is far more powerful when there are many overlapping sets.
|
|
|
