Question

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 1

Answer:

$P = \frac{1}{11}$

Explanation:

Given

$Marbles = 12$

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:

$P(1) = \frac{4}{12}$

 

Since it is a selection without replacement, there are 3 primes left and 11 marbles in total.

The probability of selecting another prime is:

$P(2) = \frac{3}{11}$

The required probability is:

$P = P(1) * P(2)$

$P = \frac{4}{12} * \frac{3}{11}$

$P = \frac{1}{11}$