Question

a plastic bag contains 5 marbles. two of the marbles are red and 3 of the marbles are blue. without looking, what is the probability of pulling out a blue marble and then another blue marble?(Assume that you don't put the first blue marble back in the bag) write your answer as a fraction.

Answer 1

$|\Omega|=5\cdot4=20\\|A|=3\cdot2=6\\\\P(A)=\dfrac{6}{20}=\dfrac{3}{10}$

Answer 2

The probability of pulling out a blue marble and then another blue marble is $\frac{2}{9}$.

Probability:

• Probability of the event, P(E) = $\frac{Favourable \ Outcomes}{Total \ Outcomes}$

How to solve the given question?

• First if we took the blue marble, so will have 5 possibilities and then picking up another blue marble we will have 4 possibilities,
  ∴ Favorable outcomes = 5 ×  4 = 20
• For the total no of outcomes, there were initially 10 marbles ( 5 blue marbles, 2 red marbles, and 3 blue marbles) as we picked up 1 marble, now we will have 9 possibilities.
  ∴ Total Outcomes = 10 × 9 = 90
• Thus the Probability,
                                  $P(E) = \frac{20}{90} = \frac{2}{9}$

Thus, the probability of pulling out a blue marble and then another blue marble is $\frac{2}{9}$.

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