SOLUTION: a bag contains 5 real diamonds and 7 fake diamonds. If 5 diamonds are picked from the bag at random, what is the probability that at least 2 of them are real?

Algebra ->  Probability-and-statistics -> SOLUTION: a bag contains 5 real diamonds and 7 fake diamonds. If 5 diamonds are picked from the bag at random, what is the probability that at least 2 of them are real?      Log On


   



Question 1154056: a bag contains 5 real diamonds and 7 fake diamonds. If 5 diamonds are picked from the bag at random, what is the probability that at least 2 of them are real?
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
There are 12%2A11%2A10%2A9%2A8=95040 that 5 diamonds can be picked. Instead of finding the probability that at least 2 diamonds are real, we can instead count the probability that 0 or 1 diamond is real and subtract from 1 to get the answer. The number of ways that all the diamonds picked are fake is 7%2A6%2A5%2A4%2A3=2520. There are 7%2A6%2A5%2A4%2A5%2A5=21000 ways to pick one real diamond. So the number of ways that at least 2 diamonds are real is 95040-%282520%2B21000%29=71520. So there is a 71520%2F95040=149%2F198 or approximately 75.25% chance that at least 2 diamonds are real.