Question

The tickets in a box are numbered from 1 to 15 inclusive. If a ticket is drawn at random and replaced and then a second is drawn at random, what is the probability that the sum of their numbers is even?

A: 49/225
B: 1/2
C: 113/225

Answer 1

I have no idea how or what to do to solve this.

Answer 2

Changed the subject to mathematics. Be sure you're posting these in the right section.

Answer 3

How do I ensure that?

Answer 4

For example, if someone is tabbed into the Mathematics section, they wouldn't see this on the question list and be able to help you, as you're putting it in Misc.

Answer 5

When you begin typing into the 'Ask a question' box in the top left, there is a white box under the bottom left corner which allows you to choose a subject. Select Mathematics/the appropriate subject.

Answer 6

Did it change now?

Answer 7

This question is a bit more abstract, I might have to actually turn on my brain.

Answer 8

And I already put it in Mathematics.

Answer 9

Oh, thank you. I'll remember that in the future.

Answer 10

So we have:

1, 2, 3, 4, 5, 6,7, 8, 9, 10, 11, 12, 13, 14, 15

odds: 1, 3, 5, 7, 9, 11, 13, 15
evens: 2, 4, 6, 8, 10, 12, 14

We have 8 odds and 7 evens.

Answer 11

So when you get:

odd + odd, the sum is an even number
odd + even, the sum is an odd number
even + even, the sum is an even number

Answer 12

How are there 225 possibilities?

Answer 13

Since there's two choices and the first choice ticket gets 'replaced' it is 15 outcomes times 15 outcomes, 15^2, which is 225.

Answer 14

If the first ticket didn't get replaced, it'd be 15 times 14.

Answer 15

so since there are more odd numbers, would that make it more likely that the sum will be odd?

Answer 16

since the odd and even make an odd

Answer 17

or would it be more likely that it'll be even because an odd and an odd make an even

Answer 18

Well when you draw a ticket there's a 8/15 chance it's odd, and a 7/15 chance it's even.

So slightly more of the time it will be odd, and it maintains that slight advantage since I assume it get's replaced with the same number it was.

And as I posted,
odd + odd, the sum is an even number
odd + even, the sum is an odd number
even + even, the sum is an even number

Answer 19

so would I multiply 8/15 and 7/15?

Answer 20

So 7 times 7 presents the 49 outcomes where two even #s were chosen

Answer 21

And 8 times 8 presents the outcomes where it's odd + odd

Answer 22

Oh so we only multiply the evens?

Answer 23

We multiply the outcomes where the sum is even

Answer 24

Remember odd + odd is even

Answer 25

1 + 3 = 4
5 + 7 = 12

Answer 26

So all outcomes for odd + odd which is 8 times 8, and all outcomes of even + even, which is 7 times 7

Answer 27

Do the math, add the sum of both outcome sets, and that should be your # of outcomes where the sum of the two tickets chosen is even.

Answer 28

so 7 times 7 = 49
15 times 15 = 225
so the answer should be 49/225?

Answer 29

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Shadow
So all outcomes for odd + odd which is 8 times 8, and all outcomes of even + even, which is 7 times 7
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 30

I'm confused lol

Answer 31

So you want the probability that the sum of the two tickets chosen is even

Answer 32

So you determine which outcomes make the sum even

Answer 33

Which is odd + odd and even + even

Answer 34

Since odd + even makes an odd #, for example: 1 + 4 = 5,
5 + 4 = 9

Answer 35

so multiply 8 times 8 and 7 times 7 and add them together?

Answer 36

Then you take all the outcomes where the tickets are odd + odd, and even + even.

Two odds is 8 times 8
Two evens is 7 times 7

Answer 37

Since there are 8 odds and 7 evens

Answer 38

I'm really sorry math is my absolute worst subject and I'm slow as it is.
so multiply 8 and 8 and 7 and 7 add them together and then 15 times 15

Answer 39

Yes with the first part being the numerator (outcomes where the sum of the ticket numbers is even) and the 15 times 15 being the denominator, or total outcomes/sample size.

Answer 40

And you're fine man

Answer 41

8*8= 64
7*7 = 49
64+49 = 113
and 15*15= 225
so the answer is 113/225?

Answer 42

Yes

Answer 43

omgosh thank you!

Answer 44

yw