A bag contains $2$ red marbles, $7$ blue marbles and $4$ green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest $10$ ooth, that both marbles drawn will be red? $\newline$ Answer:

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Q. A bag contains

2

red marbles,

7

blue marbles and

4

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

10

ooth, that both marbles drawn will be red?

\newline

Answer:

Calculate Total Marbles: Given: A bag contains $2$ red marbles, $7$ blue marbles, and $4$ green marbles. We need to calculate the probability of drawing $2$ red marbles in succession without replacement. $\newline$ First, calculate the total number of marbles in the bag. $\newline$ Total marbles = $2$ red + $7$ blue + $4$ green $\newline$ Total marbles = $13$
First Red Marble Probability: Calculate the probability of drawing the first red marble. $\newline$ Probability of first red marble = Number of red marbles / Total number of marbles $\newline$ Probability of first red marble = $\frac{2}{13}$
Second Red Marble Probability: Calculate the probability of drawing the second red marble after the first one has been drawn. $\newline$ Now there is $1$ red marble left and the total number of marbles in the bag is $12$ . $\newline$ Probability of second red marble $=$ Number of red marbles left $/$ Total number of marbles left $\newline$ Probability of second red marble $= \frac{1}{12}$
Combined Probability: Calculate the combined probability of both events happening one after the other (drawing two red marbles in succession). $\newline$ Combined probability = Probability of first red marble $\times$ Probability of second red marble $\newline$ Combined probability = $(\frac{2}{13}) \times (\frac{1}{12})$ $\newline$ Combined probability = $\frac{2}{156}$ $\newline$ Combined probability = $\frac{1}{78}$
Express Probability: To express the probability to the nearest thousandth, we can leave the fraction as is or convert it to a decimal. $\newline$ Probability to the nearest thousandth = $\frac{1}{78} \approx 0.013$ (rounded to three decimal places)