Answer:
(a)
(b)
(c)![\frac{5}{7},\frac{2}{3},\frac{3}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B7%7D%2C%5Cfrac%7B2%7D%7B3%7D%2C%5Cfrac%7B3%7D%7B5%7D)
Step-by-step explanation:
GIVEN: Miranda has a bag of marbles with
blue marbles,
white marbles, and
TO FIND: a) A Blue, then a red Preview
,b)A red, then a white Preview
,c) A Blue, then a Blue, then a Blue.
SOLUTION:
Total marbles in bag ![=7](https://tex.z-dn.net/?f=%3D7)
(a)
Probability of drawing blue marble ![=\frac{\text{total blue marble}}{\text{total marbles}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctext%7Btotal%20blue%20marble%7D%7D%7B%5Ctext%7Btotal%20marbles%7D%7D)
![=\frac{5}{7}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B7%7D)
As marble is not returned to bag,
Probability of drawing red marble ![=\frac{\text{total red marble}}{\text{total marbles}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctext%7Btotal%20red%20marble%7D%7D%7B%5Ctext%7Btotal%20marbles%7D%7D)
![=\frac{1}{6}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B6%7D)
(b)
Probability of drawing red marble ![=\frac{\text{total red marble}}{\text{total marbles}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctext%7Btotal%20red%20marble%7D%7D%7B%5Ctext%7Btotal%20marbles%7D%7D)
![=\frac{1}{7}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B7%7D)
As marble is not returned to bag,
Probability of drawing white marble ![=\frac{\text{total white marble}}{\text{total marbles}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctext%7Btotal%20white%20marble%7D%7D%7B%5Ctext%7Btotal%20marbles%7D%7D)
![=\frac{1}{6}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B6%7D)
(c)
Probability of drawing blue marble ![=\frac{\text{total blue marble}}{\text{total marbles}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctext%7Btotal%20blue%20marble%7D%7D%7B%5Ctext%7Btotal%20marbles%7D%7D)
![=\frac{5}{7}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B7%7D)
As marble is not returned to bag,
Probability of drawing second blue marble ![=\frac{\text{total blue marble}}{\text{total marbles}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctext%7Btotal%20blue%20marble%7D%7D%7B%5Ctext%7Btotal%20marbles%7D%7D)
![=\frac{4}{6}=\frac{2}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%7D%7B6%7D%3D%5Cfrac%7B2%7D%7B3%7D)
As marble is not returned to the bag
Probability of drawing third blue marble ![=\frac{\text{total blue marble}}{\text{total marbles}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctext%7Btotal%20blue%20marble%7D%7D%7B%5Ctext%7Btotal%20marbles%7D%7D)
![=\frac{3}{5}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%7D%7B5%7D)