Question

A display case contains thirty-five gems, of which ten are real diamonds and twenty-five are fake diamonds. A burglar removes four gems at random, one at a time and without replacement. What is the probability that the last gem she steals is the second real diamond in the set of four?

Then, suppose that the burglar removes 10 diamonds instead. How many real diamonds is she more likely to steal?

Answer 1

Here N=35 gems , M= 10, n=4

X= probability that the last gem she steals is the second real diamond in the set of four.

X~ Hyper geometric ( N=35, M=10, n=4)

We have to find,

P(X=2)=(McX)*(N-M c n-X)/(N c n)

=(10 c 2) *( 25 c 2)/(35 c 4)

= (45*288)/52360

= 0.2475

Suppose that the burglar removes 10 diamonds.

10 real diamonds is she more likely to steal.