marbles numbered from 1 to 12 are put in a bag. if marbles are not put back into the bag after being drawn, what is the probability of drawing two prime numbers in a row?

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]

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