a bag contains 7 red marbles, 3 blue marbles and 6 green marbles. if three marbles are drawn out of the bag…

Explanation:

Step1: Calculate total marbles

$7 + 3+6=16$

Step2: Calculate first - red probability

The probability of drawing a red marble first is $\frac{7}{16}$ since there are 7 red marbles out of 16 total marbles.

Step3: Calculate second - red probability

After drawing one red marble, there are 6 red marbles left and 15 total marbles left. So the probability of drawing a red marble second is $\frac{6}{15}$.

Step4: Calculate third - red probability

After drawing two red marbles, there are 5 red marbles left and 14 total marbles left. So the probability of drawing a red marble third is $\frac{5}{14}$.

Step5: Calculate combined probability

The probability of all three events happening is the product of their probabilities: $\frac{7}{16}\times\frac{6}{15}\times\frac{5}{14}=\frac{7\times6\times5}{16\times15\times14}=\frac{210}{3360}=\frac{1}{16}= 0.0625$

Step6: Convert to percentage

$0.0625\times100 = 6.25%$. Rounding to the nearest tenth of a percent gives $6.3%$.

Answer:

$6.3%$