Question

xander spends most of his time with his 10 closest friends. he has known 4 of his 10 friends since kindergarten. if he is going to see a movie tonight with 3 of his 10 closest friends, what is the probability that the first 2 of the friends to show up to the movie are friends he has known since kindergarten but the third is not?
1/30
9/125
12/125
1/10

Explanation:

Step1: Probability of first friend

The probability that the first - friend to show up is a friend known since kindergarten is $\frac{4}{10}$ because there are 4 friends known since kindergarten out of 10 total friends.

Step2: Probability of second friend

After one friend known since kindergarten has shown up, there are 3 friends known since kindergarten left out of 9 remaining friends. So the probability that the second friend to show up is a friend known since kindergarten is $\frac{3}{9}$.

Step3: Probability of third friend

After two friends known since kindergarten have shown up, there are 6 non - kindergarten - known friends out of 8 remaining friends. So the probability that the third friend to show up is not a friend known since kindergarten is $\frac{6}{8}$.

Step4: Overall probability

We multiply these probabilities together: $\frac{4}{10}\times\frac{3}{9}\times\frac{6}{8}=\frac{4\times3\times6}{10\times9\times8}=\frac{72}{720}=\frac{1}{10}$.

Answer:

$\frac{1}{10}$