- #1

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If i have 18 bananas and 12 apples and they have the same chance of being picked,

And i have to calculate the probability of getting 2 bananas and 2 apples then my logic tells me,

The probability of picking one banana must be 18/30 (right?) The probability of picking 2 bananas in a row must be 18/30 * 18/30 = 9/25 (right?)

The probability of picking 2 apples in a row must be

12/30*12/30 = 4/25.

The probability of picking 2 bananas and 2 apples can occur in different ways/orders can't be calculated by

(18/30 * 18/30)*(12/30*12/30) . Why is that?

I know that the only true way to calculate this problem, is to first find out how many ways i can pick 4 fruits (number of possible combinations of 4), then use the binomial coefficient to find out in which ways i can pick 2 bananas, then 2 apples and then multiply the numbers together and divide it with the total number of possible combinations. I know this because it's in my textbook, but my intuition would prefere to do it the way i did it above, so i want to understand what I'm doing wrong, and if there are perhaps a explanation to why this is the only way you can calculate this problem?