Question

A bag contains 5 red marbles, 10 white marbles, and 9 blue marbles. You draw 3 marbles out at random, without replacement. What is the probability that all the marbles are red?The probability that all the marbles are red is What is the probability that exactly two of the marbles are red?What is the probability that none of the marbles are red?

Answer 1

The probability that all the marbles are red is 5 / 1012

Step-by-step explanation:

There are in total 5 + 10 + 9 = 24 marbles. Out of these 24 marbles, 5 are red.

Now if we randomly pick the first marble, the probability that it will be red is

`(5)/(24)`

For the second marble I pick, there are now 23 marbles in the bag. Out of these 23 marbles, 4 are red ( because I already took the 5th marble out). Therefore, the probability that the second marble will be red is

`(4)/(23)`

Similarly, for the third marble, the probability that it will be red will be

`(3)/(22)`

since there are 3 red marbles out of 22 total.

Therefore, the probability that ALL three marbles together will be red is

`(5)/(24)*(4)/(23)*(3)/(22)=(60)/(12,144)`
`=(5)/(1012)`

Hence, the probability that all the marbles are red is 5 / 1012.