A bag contains $5$ red marbles, $7$ blue marbles and $2$ 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

5

red marbles,

7

blue marbles and

2

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 number of marbles: Determine the total number of marbles in the bag. $\newline$ The bag contains $5$ red marbles, $7$ blue marbles, and $2$ green marbles. To find the total, add these numbers together. $\newline$ Total marbles = $5$ red + $7$ blue + $2$ green $\newline$ Total marbles = $14$
Calculate probability of drawing green marble: Calculate the probability of drawing one green marble. Since there are $2$ green marbles and $14$ total marbles, the probability of drawing one green marble on the first draw is: Probability of first green marble $=$ Number of green marbles $/$ Total number of marbles Probability of first green marble $= \frac{2}{14}$
Calculate probability of second green marble: Calculate the probability of drawing a second green marble after one has already been drawn. $\newline$ After one green marble has been drawn, there is now $1$ green marble left and the total number of marbles in the bag is $13$ . The probability of drawing the second green marble is: $\newline$ Probability of second green marble $=$ Number of remaining green marbles $/$ New total number of marbles $\newline$ Probability of second green marble $= \frac{1}{13}$
Calculate combined probability: Calculate the combined probability of both events happening. $\newline$ To find the probability of both events happening (drawing two green marbles in a row), multiply the probabilities of each individual event. $\newline$ Combined probability = Probability of first green marble $\times$ Probability of second green marble $\newline$ Combined probability = $(2 / 14) \times (1 / 13)$ $\newline$ Combined probability = $2 / 182$
Simplify combined probability: Simplify the combined probability. $\newline$ Simplify the fraction $\frac{2}{182}$ to its lowest terms. $\newline$ Combined probability = $\frac{1}{91}$
Convert probability to percentage: Convert the probability to a percentage. $\newline$ To convert the probability to a percentage, multiply by $100$ . $\newline$ Percentage probability = Combined probability $\times 100$ $\newline$ Percentage probability = $(1 / 91) \times 100$
Calculate percentage to nearest tenth: Calculate the percentage to the nearest tenth of a percent. $\newline$ Perform the division to find the percentage. $\newline$ Percentage probability $\approx 1.0989\%$ $\newline$ To the nearest tenth of a percent, this is approximately $1.1\%$ .