Answer to Question #241569 in Statistics and Probability for liz

Question

A jar contains 4 red marbles, 5 white marbles, and 6 blue marbles. Two marbles are randomly selected from the jar with replacement. Find the following probabilities. Leave your answer as a reduced fraction.

1. A red marble and then a blue marble is randomly selected.    
   
2. A white marble and then a red marble is randomly selected. 

Answer 1

Solution:

Given: number of red marbles = 4

number of white marbles = 5

number of blue marbles = 6

Total number of marbles contain in the jar = 4 + 5 + 6 = 15

We have to select two marbles randomly from the jar with replacement.

(a):

Probability of selecting a red marble

= number of red marbles / total number of marbles

= 4 / 15

The marble is then replace back to the jar.

And

probability of selecting a blue marble

= number of blue marbles / total number of marbles

= 6 /15

Now, probability of selecting a red marble and then selecting a blue marble$=\dfrac 4{15}\times \dfrac6{15}=\dfrac8{75}$

(b):

Probability of selecting a white marbles

= number of white marbles / total number of marbles

= 5 / 15

The marble is then replace back to the jar.

And

probability of selecting a red marble

= number of red marbles / total number of marbles

= 4 / 15

Now, probability of selecting a white marble and then selecting a red marble$=\dfrac5{15}\times\dfrac4{15}=\dfrac4{45}$