The red die is irrelevant, obviously, so you can ignore it. Assuming that the blue die is six-sided and that the numbers on the sides are 1 through 6, how many of the outcomes are either a 3 or a 2, 4, or 6? (Since 3 isn't even, there can't be a "both".)Q1. Two dice are rolled , one blue and one red. how many outcomes have either the blue die 3 or an even or both?
How many are multiples of 5? How many are multiples of 7? Of course, these counts include multiples of 5*7 = 35, so some of each count are duplicates. How would you remove these? (In other words, the "or both" is already included, but is over-included. So don't worry about the "or both"; worry about removing the over-counting.)Q2: How many integers from 1 to 10,000 , inclusive , are multiples of 5 or 7 or both?
Above is that a typo & you meant on both?Q1.Two dice are rolled , one blue and one red. how many outcomes have either the blue die 3 or an even or both.
Here is a useful fact if \(\displaystyle N\) is a positive integer and \(\displaystyle 1\le k\le N\) then the number of multiples of 1 in 1 to N is \(\displaystyle \left\lfloor {\dfrac{N}{k}} \right\rfloor \). (That is the floor function.)Q2 How many integers from 1 to 10,000 , inclusive , are multiples of 5 or 7 or both?
The red die is irrelevant, obviously, so you can ignore it. Assuming that the blue die is six-sided and that the numbers on the sides are 1 through 6, how many of the outcomes are either a 3 or a 2, 4, or 6? (Since 3 isn't even, there can't be a "both".)
How many are multiples of 5? How many are multiples of 7? Of course, these counts include multiples of 5*7 = 35, so some of each count are duplicates. How would you remove these? (In other words, the "or both" is already included, but is over-included. So don't worry about the "or both"; worry about removing the over-counting.)
If you get stuck, please reply showing your work so far. Thank you!
Above is that a typo & you meant on both?
Here is a useful fact if \(\displaystyle N\) is a positive integer and \(\displaystyle 1\le k\le N\) then the number of multiples of 1 in 1 to N is \(\displaystyle \left\lfloor {\dfrac{N}{k}} \right\rfloor \). (That is the floor function.)
So the answer to this question is:
\(\displaystyle \left\lfloor {\dfrac{10^4}{5}} \right\rfloor +\left\lfloor {\dfrac{10^4}{7}} \right\rfloor -\left\lfloor {\dfrac{10^4}{35}} \right\rfloor \)
The helper was asking, not informing. Please re-check the exercise. Is the word "on" or is the word "or"? The answer to the question will depend on what the actual question was. If "or", then follow my reply. If "on", then follow the other reply. :wink:Q 1 so the question should be on both?