a bag contains 3 red marbles, 2 blue marbles and 7 green marbles. if two marbles are drawn out of the bag…
a bag contains 3 red marbles, 2 blue marbles and 7 green marbles. if two marbles are drawn out of the bag (without replacement), what is the probability, to the nearest 1000th, that both marbles drawn will be red?
Answer
Explanation:
Step1: Calculate total marbles
Total marbles = 3 (red) + 2 (blue) + 7 (green) = 12.
Step2: Calculate probability of first - red draw
Probability of first red marble, $P_1=\frac{3}{12}$.
Step3: Calculate probability of second - red draw
After drawing one red marble, there are 2 red marbles left and 11 marbles in total. So probability of second red marble, $P_2=\frac{2}{11}$.
Step4: Calculate probability of both red
Since the draws are dependent events, probability of both red is $P = P_1\times P_2=\frac{3}{12}\times\frac{2}{11}=\frac{6}{132}=\frac{1}{22}\approx0.045$.
Answer:
0.045