A bag contains $8$ red marbles, $4$ blue marbles and $5$ green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest $10$ th of a percent, that all three marbles drawn will be green? $\newline$ Answer:

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Q. A bag contains

8

red marbles,

4

blue marbles and

5

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

10

th of a percent, that all three marbles drawn will be green?

\newline

Answer:

Determine total marbles: Determine the total number of marbles in the bag. $\newline$ The bag contains $8$ red marbles, $4$ blue marbles, and $5$ green marbles. To find the total, add these numbers together. $\newline$ Total marbles = $8$ red + $4$ blue + $5$ green $\newline$ Total marbles = $17$ marbles
Calculate green marble probability: Calculate the probability of drawing one green marble. $\newline$ Since there are $5$ green marbles out of $17$ total marbles, the probability of drawing one green marble is: $\newline$ Probability of one green marble $=$ Number of green marbles $/$ Total number of marbles $\newline$ Probability of one green marble $= \frac{5}{17}$
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 $4$ green marbles left and $16$ marbles in total. $\newline$ Probability of second green marble = Number of remaining green marbles / Total remaining marbles $\newline$ Probability of second green marble = $\frac{4}{16}$
Calculate third green marble probability: Calculate the probability of drawing a third green marble after two have already been drawn. $\newline$ After drawing two green marbles, there are now $3$ green marbles left and $15$ marbles in total. $\newline$ Probability of third green marble = Number of remaining green marbles / Total remaining marbles $\newline$ Probability of third green marble = $\frac{3}{15}$
Calculate combined probability: Calculate the combined probability of drawing three green marbles in a row. $\newline$ To find the combined probability, multiply the probabilities from each of the previous steps. $\newline$ Combined probability = Probability of one green marble $\times$ Probability of second green marble $\times$ Probability of third green marble $\newline$ Combined probability = $(5 / 17) \times (4 / 16) \times (3 / 15)$ $\newline$ Combined probability = $(5 \times 4 \times 3) / (17 \times 16 \times 15)$ $\newline$ Combined probability = $60 / 4080$ $\newline$ Combined probability = $1 / 68$
Convert to percentage: Convert the probability to a percentage and round to the nearest tenth of a percent. $\newline$ To convert to a percentage, multiply the probability by $100$ . $\newline$ Percentage = Combined probability $\times 100$ $\newline$ Percentage = $(1 / 68) \times 100$ $\newline$ Percentage $\approx 1.47\%$ $\newline$ Since we need to round to the nearest tenth of a percent, the final answer is $1.5\%$ .