Question

There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a blue marble is 8/9
There are 45 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.

Answer 1

the marble is not "replaced", the probability of the second drawing changes, since there are less marbles in the jar. The probability of drawing a red marble = 2/5. The probability of drawing a blue marble is now = 1/4. The probability of drawing a red marble = 2/5.

Answer 2

Step-by-step explanation:

In simple cases, it is easy to visualize picking up balls by drawing a tree diagram. I'll skip that part.

To pick a red marble first, you have a probability 510. To pick another red marble, now you will have probability 49 (since no replacement).

To pick a blue marble next, you have probability 58, and for another 47.

Note that this is not the only way to pick up the required balls, you can have other arrangements as RRBB,RBRB,BRBR,BBRR,BRRB,RBBR, in total (42)=6 ways.