A bag contains $7$ red marbles, $5$ blue marbles and $3$ 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 red? $\newline$ Answer:

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Q. A bag contains

7

red marbles,

5

blue marbles and

3

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 red?

\newline

Answer:

Calculate Total Marbles: First, we need to determine the total number of marbles in the bag. $\newline$ Total marbles $= \text{red marbles} + \text{blue marbles} + \text{green marbles}$ $\newline$ Total marbles $= 7 + 5 + 3$ $\newline$ Total marbles $= 15$
Calculate Probability of First Red Marble: Next, we calculate the probability of drawing one red marble on the first draw. $\newline$ Probability of first red marble $= \frac{\text{Number of red marbles}}{\text{Total number of marbles}}$ $\newline$ Probability of first red marble $= \frac{7}{15}$
Update Marbles After First Draw: After drawing one red marble, there is one less red marble and one less total marble in the bag. $\newline$ New number of red marbles = Original number of red marbles $- 1$ $\newline$ New number of red marbles = $7 - 1$ $\newline$ New number of red marbles = $6$ $\newline$ New total number of marbles = Original total number of marbles $- 1$ $\newline$ New total number of marbles = $15 - 1$ $\newline$ New total number of marbles = $14$
Calculate Probability of Second Red Marble: Now, we calculate the probability of drawing a second red marble after the first one has been drawn. $\newline$ Probability of second red marble $=$ New number of red marbles $/$ New total number of marbles $\newline$ Probability of second red marble $=$ $\frac{6}{14}$
Multiply Probabilities for Both Red Marbles: To find the probability of both events happening (drawing two red marbles in a row), we multiply the probabilities of each individual event. $\newline$ Probability of both red marbles = Probability of first red marble $\times$ Probability of second red marble $\newline$ Probability of both red marbles = $(7 / 15) \times (6 / 14)$ $\newline$ Probability of both red marbles = $(7 \times 6) / (15 \times 14)$ $\newline$ Probability of both red marbles = $42 / 210$
Simplify Probability Fraction: Simplify the fraction to find the probability in its simplest form. Probability of both red marbles = $\frac{42}{210}$ Probability of both red marbles = $\frac{1}{5}$
Convert Probability to Percentage: Finally, we convert the probability to a percentage to the nearest tenth of a percent. $\newline$ Probability as a percent = Probability of both red marbles $\times 100\%$ $\newline$ Probability as a percent = $(1 / 5) \times 100\%$ $\newline$ Probability as a percent = $20\%$