Question

Suppose a jar contains 6 red marbles and 27 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Answer 1

Now the jar contains 6 red marbles and 27 blue marbles

Total number of marbles is

`6+27=33\text{ marbles }`

Now taking two red marbles at random means the first marble is red and the second marble is red.

Probability that the first marble is red is

`\begin{gathered} =\frac{\text{ number of red marbles }}{\text{ total number of marbles}} \\ =(6)/(33) \end{gathered}`

After taking the first red marble, we will have 5 red marbles remaining and a total of 32 marbles remaining

So probability of picking the second marble is

`\begin{gathered} =\frac{\text{ number of red marbles remaining }}{\text{total number of marbles remaining }} \\ =(5)/(32) \end{gathered}`

So probability both marbles are red means the first is red and the second is red.

And here means we have to multiply, this becomes

`\begin{gathered} (6)/(33)*(5)/(32) \\ =(5)/(176) \end{gathered}`

Hence the answer is

`(5)/(176)`