Question

A bag contains 6 blue marbles​, 2 red marbles​, and 2 yellow marbles. The probability of drawing a blue marble out of the bag is six tenths or 60​%. How many of what color of marbles must be added to the bag so that the probability of a blue marble being drawn at random from the bag is 75​%?

Answer 1

9 blue marbles and 1 red or yellow marble

Explanation:

Since the bag contains 6, 2, and 2 quantity of blue, red and yellow marbles respectively. It means the bag contains a total of 10marbles.

So ideally, the probability of picking a blue marble at random will be 6/10 i.e. 6blue marbles/ total number of marbles

Now, in order to have the probability of a blue marble being randomly picked out to be 75%,

We have to first convert the percentage to fraction= 75% means 75/100 , we divide both numerator and denominator by 5

We have 15/20, which means 15 blue marble / 20 total marbles

To get 75% probability, we have to have 20 total marbles by adding an additional 10. Since we are working on the probability of a blue marble being picked, it means we must add 15 - 6 = 9 blue marbles

Since 10 additional marbles must be added in total, 9 blue marbles has already been added, so we are left with 1

The 1 marble can either be a red or yellow marble.

In total we have, 10(9 blue, 1 red/yellow) + 6blue + 2red + 2yellow = 20total marbles

Probability of picking a blue marble will be, 9+6= 15 blue marbles/20 total marbles i.e 75%