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Answer:
[tex]P = \frac{1}{11}[/tex]
Explanation:
Given
[tex]Marbles = 12[/tex]
Selection: Without replacement
Required
The probability of selecting 2 primes
Between 1 and 12, the prime digits are: 3, 5, 7 and 11
i.e. 4 prime digits
When the first marble is selected, the probability that it will be prime is:
[tex]P(1) = \frac{4}{12}[/tex]
Since it is a selection without replacement, there are 3 primes left and 11 marbles in total.
The probability of selecting another prime is:
[tex]P(2) = \frac{3}{11}[/tex]
The required probability is:
[tex]P = P(1) * P(2)[/tex]
[tex]P = \frac{4}{12} * \frac{3}{11}[/tex]
[tex]P = \frac{1}{11}[/tex]