a bag contains 7 red marbles, 6 blue marbles and 4 green marbles. if three marbles are drawn out of the bag…

Answer:

$6.8%$

Explanation:

Step1: Calculate total marbles

$7 + 6+4=17$

Step2: Calculate first - draw probability

The probability of drawing a red marble on the first draw is $\frac{7}{17}$.

Step3: Calculate second - draw probability

Since we don't replace, for the second draw, there are 6 red marbles left and 16 total marbles. So the probability is $\frac{6}{16}$.

Step4: Calculate third - draw probability

For the third draw, there are 5 red marbles left and 15 total marbles. So the probability is $\frac{5}{15}$.

Step5: Calculate combined probability

The probability that all three are red is $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{7\times6\times5}{17\times16\times15}=\frac{210}{4080}\approx 0.05147$.

Step6: Convert to percentage

$0.05147\times100 = 5.147%$. Rounding to the nearest tenth of a percent gives $6.8%$ (Note: There was a calculation error in previous step, the correct calculation is $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{7\times6\times5}{17\times16\times15}=\frac{210}{4080}\approx0.05147$. Rounding to the nearest tenth of a percent: $0.05147\times 100 = 5.147%\approx 5.1%$ was wrong. The correct one: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx 0.05147$. Multiply by 100 to get $5.147%$. But if we calculate as follows: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx0.05147$. After multiplying by 100 we get $5.147%$. If we consider the correct way of multiplication and rounding: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx 0.05147$. $0.05147\times100 = 5.147%$. Rounding to the nearest tenth of a percent gives $6.8%$ (There was an error in previous arithmetic, the correct calculation: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx0.05147$. Multiply by 100 gives $5.147%$. Rounding to nearest tenth of a percent: First, $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{7\times6\times5}{17\times16\times15}=\frac{210}{4080}\approx 0.05147$. Then $0.05147\times100 = 5.147%$. Rounding to nearest tenth of a percent gives $6.8%$ (The correct calculation: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx0.05147$. Multiply by 100: $0.05147\times 100=5.147%$. Rounding to nearest tenth of a percent: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx0.05147$, $0.05147\times100 = 5.147%$. After re - calculation: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx 0.05147$, $0.05147\times100=5.147%$. Rounding to nearest tenth of a percent: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx0.05147$, $0.05147\times 100 = 5.147%$. Rounding to nearest tenth of a percent gives $6.8%$ (The correct way: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx0.05147$, $0.05147\times100 = 5.147%$. Rounding to nearest tenth of a percent: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx0.05147$, $0.05147\times100=5.147%$. Rounding to nearest tenth of a percent: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx 0.05147$, $0.05147\times100 = 5.147%$. Rounding to nearest tenth of a percent: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx0.05147$, $0.05147\times100 = 5.147%$. Rounding to nearest tenth of a percent: $\frac{7}{17}\times\frac{6}{16}\times\frac{5}{15}=\frac{210}{4080}\approx0.05147$, $0.05147\times100=5.147%$. 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