Question

Miranda has a bag of marbles with 5 blue marbles, 1 white marbles, and 1 red marbles. Find the following probabilities of Miranda drawing the given marbles from the bag if the first marble(s) is(are) not returned to the bag after they are drawn.
a) A Blue, then a red Preview
b)A red, then a white Preview
c) A Blue, then a Blue, then a Blue

Answer 1

Answer:

(a)$\frac{5}{7},\frac{1}{6}$ (b)$\frac{1}{7},\frac{1}{6}$ (c)$\frac{5}{7},\frac{2}{3},\frac{3}{5}$

Step-by-step explanation:

GIVEN: Miranda has a bag of marbles with $5$ blue marbles, $1$ 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 $=7$

(a)

Probability of drawing blue marble $=\frac{\text{total blue marble}}{\text{total marbles}}$

                                                          $=\frac{5}{7}$

As marble is not returned to bag,

Probability of drawing red marble  $=\frac{\text{total red marble}}{\text{total marbles}}$

                                                         $=\frac{1}{6}$

(b)

Probability of drawing red marble $=\frac{\text{total red marble}}{\text{total marbles}}$

                                                          $=\frac{1}{7}$

As marble is not returned to bag,

Probability of drawing white marble  $=\frac{\text{total white marble}}{\text{total marbles}}$

                                                         $=\frac{1}{6}$

(c)

Probability of drawing blue marble $=\frac{\text{total blue marble}}{\text{total marbles}}$

                                                          $=\frac{5}{7}$

As marble is not returned to bag,

Probability of drawing second blue marble  $=\frac{\text{total blue marble}}{\text{total marbles}}$

                                                                         $=\frac{4}{6}=\frac{2}{3}$

As marble is not returned to the bag

Probability of drawing third blue marble   $=\frac{\text{total blue marble}}{\text{total marbles}}$

                                                                    $=\frac{3}{5}$