Question

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. ??

Thanks !!

Answer 1

Hi..

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:

, 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 ..

or 45%.

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