Answer:
A.
[tex]\dfrac{6}{55}[/tex]
B.
[tex]\dfrac{6}{55}[/tex]
C.
[tex]\dfrac{4}{165}[/tex]
Step-by-step explanation:
Dustin has a bag of marbles with 4 blue marbles, 4 white marbles, and 3 red marbles. There are 11 marbles in total.
A. The probability that the first marble drawn is blue marble is
[tex]\dfrac{4}{11},[/tex]
the probability that the second marble drawn is red marble is
[tex]\dfrac{3}{10}[/tex]
The probability that the first marble drawn is blue and the second is red is
[tex]\dfrac{4}{11}\cdot \dfrac{3}{10}=\dfrac{12}{110}=\dfrac{6}{55}[/tex]
B. The probability that the first marble drawn is red marble is
[tex]\dfrac{3}{11},[/tex]
the probability that the second marble drawn is white marble is
[tex]\dfrac{4}{10}[/tex]
The probability that the first marble drawn is red and the second is white is
[tex]\dfrac{3}{11}\cdot \dfrac{4}{10}=\dfrac{12}{110}=\dfrac{6}{55}[/tex]
C. The probability that the first marble drawn is blue marble is
[tex]\dfrac{4}{11},[/tex]
the probability that the second marble drawn is blue marble is
[tex]\dfrac{3}{10},[/tex]
the probability that the third marble drawn is blue marble is
[tex]\dfrac{2}{9},[/tex]
The probability that the first, second and third marbles drawn are blue is
[tex]\dfrac{4}{11}\cdot \dfrac{3}{10}\cdot \dfrac{2}{9}=\dfrac{24}{990}=\dfrac{4}{165}[/tex]
