# Probability Permutations

Melody randomly selected 2 apples without replacing the first apple from a crate containing 10 Granny Smith apples, 14 Red Delicious apples and 18 Braeburn apples. What is the probability that Melody slected a Golden Delicious apple first and a granny Smith apple second?

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Welcome to MSE! It helps if you share your thoughts and what you have tried. Regards –  Amzoti Apr 18 '13 at 0:30
Zero. No Golden Delicious in the crate. –  André Nicolas Apr 18 '13 at 0:56

If it really says Red Delicious and then Golden Delicious it could be (a) a typo or (b) a trick question.

Let us assume it is a typo, and that the intended question asks for the probability she draws a Red Delicious, then a Granny Smith.

The probability that the first apple she draws is a Red Delicious is $\dfrac{14}{42}$.

Once she has drawn that apple, the crate contains $41$ apples, of which $10$ are Granny smith. So given that she first got a Golden Delicious, the probability the next apple is a Granny Smith is $\dfrac{10}{41}$.

Thus the probability of Golden Delicious then Granny Smith is $\dfrac{14}{42}\cdot \dfrac{10}{41}$.

This fraction can be simplified if you wish.

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Let $A$ be the event that Melody selects a Golden Delicious Apple (and replaces it.)

Let $B$ be the event that Melody selects a Granny Smith Apple (and replaces it.)

$$P(A)=\dfrac{\bullet}{\bullet}$$

Now,

$$P(B|A) = P(B) = \dfrac{\bullet}{\bullet}$$

Required Probability = $$P(A)\times P(B|A)=P(A)\times P(B)=\bullet$$

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