Question

Three numbers are extracted randomly from the set {1,2,3, ..., 40}. What is the probability that the product of the extracted numbers is an odd number?

Answer 1

First of all, figure out the general rules for multiplying odd/even numbers

Answer 2

well the probabilty of this becoming an odd number is to... yeah what wio said

Answer 3

For example \(2n\times 2m = 4mn = 2(2mn)\) so even times even is even

Answer 4

Odd times odd is odd.
Even times odd is even.

Answer 5

So, even there is even one even number, the whole product is even

Answer 6

So the question simplifies to: What is the probability that all numbers selected are odd.

Answer 7

@pain100 Have I helped enough, or shall I continue?

Answer 8

aaaaaa..... i dont get it at all sorry

Answer 9

What do you not understand?

Answer 10

it seas ,Three numbers are extracted randomly,then
what is the probability that the product of the extracted numbers is an odd numberand i dont know how to write this down

Answer 11

Okay, do you know what a product is?

Answer 12

yea

Answer 13

An example is if they took out 1, 2, and 3.

Answer 14

The product would be 6, which is even

Answer 15

yea,but how many combinations do i have to do to answer this,isnt there a formula or something

Answer 16

i need to find the odd numbers,and there are soo many combinations

Answer 17

Okay sure...

Answer 18

But my point is, if you want the product to be odd, all the numbers you pick need to be odd. Does that make sense?

Answer 19

This will help us solve the problem

Answer 20

yea,i get than,but i dont pick the numbers,they are randomly extracted

Answer 21

Now, how many numbers are there in the set in total?

Answer 22

40

Answer 23

How many of the numbers in it are odd?

Answer 24

20 i think

Answer 25

So what is the probability of picking one odd number?

Answer 26

20/40

Answer 27

Now, suppose we already take out an odd number.
What are the total numbers in the set, and how many are odd?

Answer 28

19

Answer 29

and the total numbers in the set?

Answer 30

39

Answer 31

So, after we pick out and odd number, what is the probability that the second one we pick will be odd?

Answer 32

19/39

Answer 33

Yes, and for the third one?

Answer 34

and the third 18/38

Answer 35

So, what is the probability that all three of these events happen, and we pick 3 odd numbers?

Answer 36

(20/40)*(19/39)*(18/38)

Answer 37

So in the end, you are able to do the problem.

Answer 38

There wasn't any set formula... you had to be a bit clever. That is all

Answer 39

thanks