Suppose a jar contains 5 red marbles and 25 blue marbles. If you reach in the jar and pull out one marble at random, do not replace the marble, and reach in the jar to pull out a second marble. Find the probability that both are red. Write your answer as a reduced fraction.

Probability that event will have both red marbles will be 2.3% or 0.023.

Step-by-step explanation:

Given:

Total red marbles=5

Total blue marbles=25

Total number of marbles = 30

To Find:

The probability that both are red without replacement of marbles.

Solution:

Now

Total sample space is 30 and total red marbles are 5

For a event that getting red marble probability is,

=Total red marbles / total marbles.

=5/30

=1/6

So probability if getting red marble is 1/6

Now for second chance there will be 4 red marbles remaining and 29 total marbles so,

In second chance probability if getting red marble will be

=total red marbles present/total marbles remaining

=4/29

Now,

The required probability will be getting both at a time

i. e probability getting red AND red marble so here AND operator which means multiple both the probability.

Probability both will have red = 1/6*4/29

=4 / (29*6) = 2 / (29*3)

=0.022988

=0.023

=2.3 %