I'll be needing some help AGAIN.. Yeah I know sorry
but this is really my weak point..
Renee has a bag of 6 candies, 4 of which are sweet and 2 of which are sour.
Jack picks two candies simultaneously and at random. What is the chance
that exactly 1 of the candies he has picked is sour?
Here's what I did: I thought why not use combinatorics lol (too brave right?
). So I thought there are 6!/4!2! = 15 ways to pick 2 candies out of the 6.
I need exactly 1 sour so the chance of getting exactly 2 sour was 4/15. 1-4/15 = 11/15. This was SOOO WRONG !!
Here's the answer:
2/6 x 4/5 = 8/30 (sour fist and then sweet)
2/6 x 4/5 = 8/30 (sweet fist and then sour)
8/30 + 8/30 = 16/30 = 8/15.
Is it just coincidence that I got 15 out of my nCr calculation? Can someone explain to me if this can also be calculated using combinatorics? I think the reason I used the nCr is because during praciticing on some probab. questions I saw more than a few questions being answered using combinatorics and somehow it seemed easier to me..
Thanks you guys, appreciate it!
You were right in calculating Total Possible ways to pick two candies.
Total = 6C2 = 6*5/2 = 15
Pick 1 sour candy out of 2 sour candy
Pick 1 sweet candy out of 4 sweet candy
2C1*4C1 = 2*4=8
When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters.
Probability of choosing sour candy first AND Probability of choosing sweet candy
Probability of choosing sweet candy first AND Probability of choosing sour candy
2/6* 4/5 + 4/6 * 2/5
= 8/30 + 8/30
Why: 2/6* 4/5 + 4/6 * 2/5
P=2/6: total sour candies= 2, total candies=6
1 Sour candy Picked.
AND means "*"
Now, total candies=5(because one picked). Sweet candies=4(First picked was sour so 4 sweet candies still left)
2/6 * 4/5
OR Means "+"
4/6: total sweet candies= 4, total candies=6
1 Sweet candy Picked.
AND means "*"
Now, total candies=5(because one picked). Sour candies=2(First picked was sweet so 2 sour candies still left)
4/6 * 2/5
Does that make little sense?