Question

maria had a bag that contained 2 blue marbles, 3 green marbles, 4 red marbles, 5 yellow marbles, and 6 orange marbles. maria removed one marble without looking and she recorded the result. she then removed a second marble without replacing the first marble.
what is the probability that maria removed a red marble followed by a yellow marble?
a. $\frac{3}{80}$
b. $\frac{1}{20}$
c. $\frac{1}{19}$
d. $\frac{9}{20}$
e. $\frac{3}{100}$

Explanation:

Step1: Calculate the total number of marbles initially

The total number of marbles is \(2 + 3+4 + 5+6=20\) marbles.

Step2: Calculate the probability of drawing a red marble first

The probability of drawing a red marble is \(\frac{4}{20}\) (since there are 4 red marbles out of 20 total).

Step3: Calculate the probability of drawing a yellow marble second

After removing one red marble, there are \(20 - 1=19\) marbles left. The probability of drawing a yellow marble is \(\frac{5}{19}\) (since there are 5 yellow marbles left).

Step4: Calculate the combined probability

Since these are independent - sequential events (without replacement), we multiply the probabilities. \(\frac{4}{20}\times\frac{5}{19}=\frac{4\times5}{20\times19}=\frac{20}{380}=\frac{1}{19}\)

Answer:

C. \(\frac{1}{19}\)