Basic Probability: choosing without replacement

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The problem involves calculating the probability of selecting a red apple after two green apples have been chosen from a box containing 22 red and 3 green apples. After removing the two green apples, 23 apples remain, including 22 red ones. The probability of the third apple being red is therefore 22 out of 23. The solution confirms that the calculated probability of 22/23 is correct. This highlights the concept of probability in scenarios of selection without replacement.
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Homework Statement



A box contains 22 red apples and 3 green apples. 3 apples are selected at random, one after the other, without replacement.

(a) The first two apples are green. What is the probability that the 3rd apple is red?


Homework Equations





The Attempt at a Solution



well if the first two are green, that means 2 of the 25 total apples are gone, so 23 remain. You have 22 red apples to choose from out of a total of 23.

Thus, I got P= 22/23

Correct?
 
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