# A paper bag contains 20 slips of paper, 8 are blue and were numbered 1-=8 and there are twelve pink slips numbered 9--20. What is the probability of selecting a pink slip or a multiple of ...

A paper bag contains 20 slips of paper, 8 are blue and were numbered 1-=8 and there are twelve pink slips numbered 9--20. What is the probability of selecting a pink slip or a multiple of 4. What is the probability of selecting a blue slip or the number 18.

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### 3 Answers

Since the blue slips are numbered 1 through 8, there are 8 blue slips of paper and 12 pink slips of paper. Thus, there are 12 possible ways to select a pink slip.

Since there are 20 pieces of paper numbered 1 through 20, there are 5 pieces of paper that are numbered as a multiple of 4: 4, 8, 12, 16, and 20. The first two are blue and the last three are pink. So there are 5 ways to select a multiple of 4. However, 3 of them are already counted because they are among the 12 pink slips of paper.

To summarize, there are 12 ways to get "a pink" and 5 ways to get "a multiple of 4". These two events overlap, because there are three pink multiples of 4. This means, the total number of ways to get EITHER "a pink" OR "a multiple of 4" is

12 + 5 - 3 = 14.

Three pink multiples of 4 have to be subtracted because in 12 + 5 they are counted twice.

The probability of selecting a pink slip or a multiple of 4 is then the ratio of the number of ways of picking the above (14) to the total number of slips of paper:

`14/20 = 7/10` , or 70%.

**The probability of selecting a pink slip or a multiple of 4 is 7/10, or 70%.**

The number of ways to select a blue slip of paper is 8, since there are 8 blue slips. There is only one way to select the number 18. These two events do not overlap, because the number 18 is on the pink slip of paper. So there are 8 + 1 = 9 ways to obtain the desired result (EITHER blue slip OR the number 18.)

So the probability of the above result will be `9/20`

or 45%.

**The probability of selecting a blue slip or the number 18 is 9/20, or 45%.**

First I'd like to mention that there are 12 pink slips and only 11 # between 9 & 20, and although this doesn't aid the problem any, if taken into consideration it could definitely complicate things, since it means that there is either a pink slip with no # or one # is doubled.

Secondly, probability is just the ratio of the number of items your checking for over the total. Therefore, the probability of pulling a pink paper is 12/20, or 60% ((12 divided by 20) * 100 = 60%), and the probability of pulling a blue is 8/20, or 40%.

There are 5 multiples of 4 in this bag: 4, 8, 12, 16, 20. Therefore the chances of pulling one is 5/20 or 25%. Now unless that unknown slip of paper is an extra 18, there should only be 1 18 in the bag, so the probability of pulling it is 1/20 or 5%.

Probability = Part / Whole

Since there are 20 slips in total and the ones that are pink are numbered 9-20, there are 12 pink slips to choose from. This means the probability for a pink slip is 12/20, which simplifies to 3/5. The multiples of 4 between 1 and 20 are 4, 8, 12, 16, and 20. That means there are 5 chances of getting a multiple of four. The probability would be 5/20, or 1/4.

To get the probability that the slip will be pink *or* be a multiple of four, you have to take 12 (pink slips) plus 5 (multiples of 4) and then subtract 3. You subtract 3 because that's how any slips are pink AND have a multiple of four which overlap and can't be counted. This gives you a probability of 14/20 or **7/10**.

Since it says there are 8 blue slips of paper out of 20 total, the probability you would get a blue slip is 8/20, which simplifies to 2/5. Out of all the slips there is only one marked with the number 18, so the probability you'd get that slips is 1/20.

So the probability of getting a blue slip *or* the number 18 would be found by adding 8 (blue slips) and 1 (the slip with 18). This gives you a probability of **9/20**. You don't have to subtract because anything because there is no blue slip with the number 18 and nothing overlaps.