There are 4 red and 8 blue marbles in a bag. Mark draws a blue marble out of the bag and does not replace it. Mark draws a second blue marble out of the bag and does not replace it.
What is the probability that the next marble he draws will also be blue?
Answer options with 4 options
A.
2-thirds
B.
3-fourths
C.
3-fifths
D.
1-sixth
To solve this problem, we need to consider the probability of each event separately and then multiply them together.
First, Mark draws a blue marble out of the bag. There are a total of 4 + 8 = 12 marbles in the bag, so the probability of drawing a blue marble initially is 8/12 = 2/3.
After the first blue marble is drawn, there are now 4 red and 7 blue marbles left in the bag. Therefore, the probability of drawing a second blue marble is 7/11.
To find the probability of drawing a third blue marble, we can now calculate the probability of drawing a blue marble from the remaining marbles in the bag. After the second blue marble is drawn, there are 4 red and 6 blue marbles left in the bag, so the probability is 6/10 = 3/5.
To find the overall probability of drawing a blue marble in all three events, we multiply the probabilities together:
(2/3) * (7/11) * (3/5) = 42/165
Simplifying this fraction, we get that the probability of drawing a blue marble in the next draw is 14/55.
The closest answer option to 14/55 is C. 3-fifths. Therefore, the correct answer is C.