Question

A box contains 35 gems, of which 10 are real diamonds and 25 are fake diamonds. Gems are randomly taken out of the box, one at a time without replacement. What is the probability that exactly 2 fakes are selected?

Answer 1

Answer:

$Probability = 0.504$

Step-by-step explanation:

Given

$Gems= 35$

$Real = 10$

$Fake = 25$

Required

Determine the probability of selecting two fakes

The probability can be represented as thus: $P(Fake\ and\ Fake)$

Using the following probability formula, we have:

$P(Fake\ and\ Fake) = P(Fake) * P(Fake)$

Each probability is calculated by dividing number of fakes by total number of gems:

$P(Fake\ and\ Fake) = \frac{25}{35} * \frac{25-1}{35-1}$

The minus 1 (-1) represent the numbers of fake and total gems left after the first selection

$P(Fake\ and\ Fake) = \frac{25}{35} * \frac{24}{34}$

$P(Fake\ and\ Fake) = \frac{5}{7} * \frac{12}{17}$

$P(Fake\ and\ Fake) = \frac{60}{119}$

$P(Fake\ and\ Fake) = 0.504$

Hence, the required probability is approximately 0.504