Basic Probability: choosing without replacement

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SUMMARY

The probability of selecting a red apple as the third apple after two green apples have been chosen without replacement from a box containing 22 red apples and 3 green apples is calculated as follows: After removing the two green apples, 23 apples remain, of which 22 are red. Therefore, the probability is definitively P = 22/23. This conclusion is confirmed as correct based on the established principles of probability.

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  • Understanding of basic probability concepts
  • Knowledge of combinatorial selection without replacement
  • Familiarity with probability notation and calculations
  • Ability to interpret and solve simple probability problems
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  • Study the concept of conditional probability in depth
  • Learn about combinatorial methods in probability
  • Explore advanced probability topics such as Bayes' theorem
  • Practice problems involving probability with and 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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