web2.0calc
 

Melody

avatar
यूजर का नामMelody
स्कोर118692
Membership
Stats
सवाल 900
जवाब 33647

-6
837
3
avatar+118692 

WELCOME BACK CPHILL !


●●●
Melody  11 Feb 2022
 #4
avatar+118692 
0
tap_sheep:

Two cards are drawn at random from a pack of 8 cards numbered from 1 to 8. Find the conditional probability that:

(a) the sum of the two numbers is odd given that their product is even.
(b) the product of the two numbers is odd given that their sum is even.


---------------------------------------------------------------------------------------------------------------------------------------------------------------
Thanks for your answer Rom. I am not as good at probablity as I should be and I got in a bit of a pickle when I tried this myself.
I am really just thinking allowed here. (as you said, order is not important anywhere here)

Total number of possible combinations = 8C2 = 28
Number of EE combinations = 4C2 = 6
Number of OO combinations = 4C2 = 6
Number of EO combinations = 4C1 * 4C1 = 4*4 = 16

(a) the sum of the two numbers is odd given that their product is even.
the product is even if the cards are EE or EO.
There are 6+16 = 22 of these combinations.
Of these combinations the sum will be odd if the cards are OE. There are 16 of these.
Therefore the probability that the sum of the two numbers is odd given that their product is even must be 16/22 = 8/11
(this is only different because you made a tiny adding error that tap_sheep could easily have picked up on him/herself. It is of no consequence.

b) Find the conditional probability that the product of the two numbers is odd given that their sum is even.
The sum is even if the numbers are EE or OO. There are 2+6=12 of these
The product is odd if the numbers are OO. There are 6 of these.
so the conditional probability that the product of the two numbers is odd given that their sum is even is 6/12 =1/2

Thank you for that lesson Rom.

I was actually thinking that maybe we could have a continuing thread dealing only with probability. I really need more practice. What do you think Rom?
Would anyone else like to comment or organise the thread?
2 Feb 2014
 #25
avatar+118692 
+14
*
Hi all,
It was a quiet weekend day today.
There were a couple of good answers from Rom and Keltoi. Thanks guys, your answers are much appreciated.
I like Serena gave the forum a great parametric equation to use in Desmos Graphing calculator. You will have to actually use it if you want to know what it is
I put out a post reminding the question presenters that good manners are always appreciated. i will bump this up in front of this post. I don't know how much difference it will make but it can't hurt to remind people every now and then.
There is one unanswered question, it is called "Pearson's r and coefficient of determination" by Shoni. I will bump it up so that it is easy to find. If no one can help her she will need to be referred to a different forum.
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Now, our new adult mathematicans are I like Serena, Reinout-g and Rom. I would like to introduce you all to Kitty<3.
In the weeks prior to you joining this forum Kitty was my right hand girl, I really don't think I could have coped without her.
She is a sophomore student, which to the best of my understanding is just pre-calculus. Kitty answered many of the junior High questions.
Her answers are always of an extremely high quality.

She wasn't on the forum much last week so i wrote and asked her how she was feeling about the changes that have taken place.
This was her reply.

"I would agree that this forum would work better for mostly younger people who have simpler math questions, as there are quite a lot of physics and higher-level math forums out there. But it's nice that more adults are helping out here now. Personally, I didn't really feel left out, just busy and bombarded with essays and homework.
It would hopefully work out beautifully if the kids could answer and the adults could help check the answers. That, as you said, is an important role, and both the kids and the new adults could help out "

I just wanted to introduce Kitty<3 because i think that it is important that all the key answer providers recognise each other.
Good night all.
2 Feb 2014