document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #776571 by Shin123(626) $\"\"$ $\"About$

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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. \n" ); document.write( "

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