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notka56 [123]
3 years ago
11

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?
Mathematics
1 answer:
USPshnik [31]3 years ago
7 0

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

<em>Hence, the required probability is approximately 0.504</em>

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