l0rrie wrote:

Hi everyone,

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.

P= Favorable/Total

Total = 6C2 = 6*5/2 = 15

Favorable:

Pick 1 sour candy out of 2 sour candy

AND

Pick 1 sweet candy out of 4 sweet candy

2C1*4C1 = 2*4=8

P=8/15

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.

Thus,

Total Probability:

Probability of choosing sour candy first AND Probability of choosing sweet candy

OR

Probability of choosing sweet candy first AND Probability of choosing sour candy

2/6* 4/5 + 4/6 * 2/5

= 8/30 + 8/30

= 16/30

= 8/15

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)

P=4/5

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)

P=2/5

4/6 * 2/5

Does that make little sense?

_________________

~fluke

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