Question

a bag contains 4 red marbles, 3 blue marbles and 6 green marbles. if two marbles are drawn out of the bag (without replacement), what is the probability, to the nearest thousandth, that both marbles drawn will be red?

Explanation:

Step1: Find total number of marbles

Total marbles = 4 (red) + 3 (blue) + 6 (green) = 13.

Step2: Probability of first red marble

Probability of drawing a red marble first is $\frac{4}{13}$.

Step3: Probability of second red marble (without replacement)

After drawing one red marble, there are 3 red marbles left and total 12 marbles. So probability is $\frac{3}{12}$.

Step4: Multiply the probabilities

Since the two events are dependent, we multiply the probabilities: $\frac{4}{13} \times \frac{3}{12} = \frac{12}{156} = \frac{1}{13} \approx 0.077$.

Answer:

0.077