Answer:
[tex]Probability = 0.504[/tex]
Step-by-step explanation:
Given
[tex]Gems= 35[/tex]
[tex]Real = 10[/tex]
[tex]Fake = 25[/tex]
Required
Determine the probability of selecting two fakes
The probability can be represented as thus: [tex]P(Fake\ and\ Fake)[/tex]
Using the following probability formula, we have:
[tex]P(Fake\ and\ Fake) = P(Fake) * P(Fake)[/tex]
Each probability is calculated by dividing number of fakes by total number of gems:
[tex]P(Fake\ and\ Fake) = \frac{25}{35} * \frac{25-1}{35-1}[/tex]
The minus 1 (-1) represent the numbers of fake and total gems left after the first selection
[tex]P(Fake\ and\ Fake) = \frac{25}{35} * \frac{24}{34}[/tex]
[tex]P(Fake\ and\ Fake) = \frac{5}{7} * \frac{12}{17}[/tex]
[tex]P(Fake\ and\ Fake) = \frac{60}{119}[/tex]
[tex]P(Fake\ and\ Fake) = 0.504[/tex]
Hence, the required probability is approximately 0.504
