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3 years ago

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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?

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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Just choose 2 numbers from {1,2,3,4,5,6,7,8,...} and make sure the one you input for x is larger.

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Step-by-step explanation:

We need to choose 2 positive integers for x and y where x>y.

Positive integers are {1,2,3,4,5,6,7,.....}.

I'm going to start with (x,y)=(2,1).

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I'm going to choose (x,y)=(4,3).

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$(25+16)^2=(25-16)^2+(40)^2$

$(41)^2=(9)^2+(40)^2$

Another is (9,40,41).

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