Question

a bag contains 5 red, 3 brown, 6 yellow, and 2 blue marbles. once a marble is selected, it is not replaced. this is an example of dependent events because the second and third marble selections depend on what was selected previously. find p(brown, then brown, then not yellow) 1/280 1/40 45/2048 1/70

Explanation:

Step1: Calculate total marbles initially

The total number of marbles initially is $5 + 3+6 + 2=16$.

Step2: Calculate probability of first - brown marble

The probability of selecting a brown marble first is $P_1=\frac{3}{16}$ since there are 3 brown marbles out of 16 total marbles.

Step3: Calculate probability of second - brown marble

After one brown marble is selected, there are 2 brown marbles left and 15 total marbles left. So the probability of selecting a second brown marble is $P_2=\frac{2}{15}$.

Step4: Calculate probability of third - non - yellow marble

After two brown marbles are selected, there are 14 total marbles left. The number of non - yellow marbles is $14 - 6=8$. So the probability of selecting a non - yellow marble is $P_3=\frac{8}{14}=\frac{4}{7}$.

Step5: Calculate the combined probability

Since these are dependent events, the probability $P = P_1\times P_2\times P_3$. Substitute the values: $P=\frac{3}{16}\times\frac{2}{15}\times\frac{4}{7}=\frac{3\times2\times4}{16\times15\times7}=\frac{24}{1680}=\frac{1}{70}$.

Answer:

D. $1/70$