Question

Dustin has a bag of marbles with 4 blue marbles, 4 white marbles, and 3 red marbles.

Answer 1

Answer:

A.

$\dfrac{6}{55}$

B.

$\dfrac{6}{55}$

C.

$\dfrac{4}{165}$

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

$\dfrac{4}{11},$

the probability that the second marble drawn is red marble is

$\dfrac{3}{10}$

The probability that the first marble drawn is blue and the second is red is

$\dfrac{4}{11}\cdot \dfrac{3}{10}=\dfrac{12}{110}=\dfrac{6}{55}$

B. The probability that the first marble drawn is red marble is

$\dfrac{3}{11},$

the probability that the second marble drawn is white marble is

$\dfrac{4}{10}$

The probability that the first marble drawn is red and the second is white is

$\dfrac{3}{11}\cdot \dfrac{4}{10}=\dfrac{12}{110}=\dfrac{6}{55}$

C. The probability that the first marble drawn is blue marble is

$\dfrac{4}{11},$

the probability that the second marble drawn is blue marble is

$\dfrac{3}{10},$

the probability that the third marble drawn is blue marble is

$\dfrac{2}{9},$

The probability that the first, second and third marbles drawn are blue is

$\dfrac{4}{11}\cdot \dfrac{3}{10}\cdot \dfrac{2}{9}=\dfrac{24}{990}=\dfrac{4}{165}$