Question

A bag contains 8 white marbles, 6 red marbles and 4 blue marbles. How many blue marbles must be added to the bag so that the probability of choosing a blue marble is 1/2?

Answer 1

The actual answer would be 10 marbles.

Explanation:

1. we had started off by adding 8+4+6 to get the total number of marbles. If we do that, we will get that there are 18 marbles in total.

2. here is where the others went wrong. If we say that we need 5 blue marbles to get 9/18 blue marbles, you are wrong. This is because we have to add 5 to the total number of marbles as well. Then we get 9/23 marbles. which is clearly not 1/2,

3. However, if we multiply 5 by 2, we get 10 blue marbles. if we add 10 to the original 18, we get 28 total marbles. Now if we add 10 to 4 we get 14 blue marbles.

SUCCESS!!!

14/28 blue marbles is 1/2, therefore we must add 10 blue marbles.

Answer 2

5 marbles

Explanation:

A bag contains

8 white marbles

6 red marbles

4 blue marbles.

Total number of marbles is :

8 + 6 + 4

= 18 marbles

Based on this current proportion

The Probability of choosing a blue marble = Number of blue marbles/ Total number of marbles

In order for the Probability of choosing a blue marble to be 1/2

The number of blue marbles has to be:

= 18 marbles × 1/2

= 9 blue marbles

From the question we have 4 blue marbles, hence:

9 blue marbles - 4 blue marbles

= 5 blue marbles

Therefore, 5 blue marbles must be added to the bag so that the probability of choosing a blue marble is 1/2.