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?
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\(P(Sour=1)=\frac{C^1_4*C^1_2}{C^2_6}=\frac{8}{15}\)

OR:

\(P(Sour=1)=2*\frac{4}{6}*\frac{2}{5}=\frac{8}{15}\), multiplying by 2 as Sour/Sweet can occur in two ways: Sour/Sweet and Sweet/Sour.

Answer: C.
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Mathematically the probability of picking two balls simultaneously, or picking them one at a time (without replacement) is the same.
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We are asked to find the probability that exactly 1 of the candies he has picked is sour not at least 1.
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Collection of Questions:
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