A bag contains $3$ red marbles, $5$ blue marbles and $6$ green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest $1$ oth of a percent, that both marbles drawn will be green? $\newline$ Answer:

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Q. A bag contains

3

red marbles,

5

blue marbles and

6

green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest

1

oth of a percent, that both marbles drawn will be green?

\newline

Answer:

Determine total marbles: Determine the total number of marbles in the bag. $\newline$ The bag contains $3$ red marbles, $5$ blue marbles, and $6$ green marbles. To find the total, add these numbers together. $\newline$ Total marbles = $3$ red + $5$ blue + $6$ green = $14$ marbles.
Calculate green marble probability: Calculate the probability of drawing one green marble. Since there are $6$ green marbles out of a total of $14$ , the probability of drawing one green marble is $\frac{6}{14}$ .
Calculate second green marble probability: Calculate the probability of drawing a second green marble after one has already been drawn. $\newline$ After drawing one green marble, there are now $5$ green marbles left and a total of $13$ marbles in the bag. The probability of drawing a second green marble is now $\frac{5}{13}$ .
Calculate both events probability: Calculate the probability of both events happening together (drawing two green marbles in a row). $\newline$ To find the probability of both events happening, multiply the probabilities of each event. $\newline$ Probability of both green marbles = $(\frac{6}{14}) \times (\frac{5}{13})$ .
Perform multiplication: Perform the multiplication to find the probability. $\newline$ Probability of both green marbles = $(\frac{6}{14}) \times (\frac{5}{13}) = (\frac{6 \times 5}{14 \times 13}) = \frac{30}{182}$ .
Simplify fraction: Simplify the fraction to its lowest terms. $\newline$ $\frac{30}{182}$ can be simplified by dividing both the numerator and the denominator by $2$ . $\newline$ Simplified probability = $\frac{15}{91}$ .
Convert to percentage: Convert the probability to a percentage. $\newline$ To convert to a percentage, divide $15$ by $91$ and then multiply by $100$ . $\newline$ Percentage = $(\frac{15}{91}) \times 100$ .
Perform division and multiplication: Perform the division and multiplication to find the percentage. $\newline$ Percentage = $(\frac{15}{91}) \times 100 \approx 16.4835\%$ .
Round to nearest tenth: Round the percentage to the nearest tenth of a percent. $\newline$ Rounded percentage = $16.5\%$ .