Answer: 8.3%
Step-by-step explanation:
To find the probability that both marbles drawn will be red, we need to find the probability of drawing a red marble on the first draw and then drawing another red marble on the second draw.
Total number of marbles in the bag = 3 red + 2 blue + 4 green = 9 marbles
Probability of drawing a red marble on the first draw:
P(Red₁) = (Number of red marbles) / (Total number of marbles) = 3/9 = 1/3
After drawing one red marble, there are now 2 red marbles left in the bag and 8 marbles total.
Probability of drawing a red marble on the second draw:
P(Red₂) = (Number of red marbles left) / (Total number of marbles left) = 2/8 = 1/4
Now, we need to find the probability of both events happening. We do this by multiplying the individual probabilities:
P(Red₁ and Red₂) = P(Red₁) × P(Red₂) = (1/3) × (1/4) = 1/12
Now let's convert this fraction to a percentage, rounded to the nearest 10th of a percent:
(1/12) × 100 ≈ 8.3%
So, the probability of drawing two red marbles consecutively is approximately 8.3%.