SOLUTION: 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?

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.

RELATED QUESTIONS
Suppose you are asked to pick 3 numbers from 1 to 20 to win a prize. What is the... (answered by stanbon)

Suppose you are asked to pick 3 numbers from 1 to 20 to win a prize. What is the... (answered by ewatrrr)

Ask a person to pick a number from 1 to 10. Question:�What is the probability that a... (answered by mathmate)

Ask someone to pick a number from 1 to 20 1. What is the probability that your friend... (answered by ewatrrr)

A box contains ten balls numbered from 1 to 10. If you pick two balls at random, what is... (answered by galactus,Alan3354)

There are 15 cards, numbered 1 through 15. If you pick a card, what is the probability... (answered by stanbon)

A given state has a wonderball lottery where you pick 6 numbers from 1-51. Then out of 12 (answered by stanbon)

Many states in U.S.A have a lottery game, usually called a Pick-4, in which you pick a... (answered by ikleyn)

each of the numbers from 1 t0 10 is written on a slip of paper. Suppose you pick one... (answered by ikleyn)