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.

Question

03-11-2022
Mathematics

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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.

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HoseaY410496 HoseaY410496 · Answer 1 · 2022-11-03T10:23:36+01:00

SOLUTION

Now the jar contains 6 red marbles and 27 blue marbles

Total number of marbles is

[tex]6+27=33\text{ marbles }[/tex]

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

[tex]\begin{gathered} =\frac{\text{ number of red marbles }}{\text{ total number of marbles}} \\ =\frac{6}{33} \end{gathered}[/tex]

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

[tex]\begin{gathered} =\frac{\text{ number of red marbles remaining }}{\text{total number of marbles remaining }} \\ =\frac{5}{32} \end{gathered}[/tex]

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

[tex]\begin{gathered} \frac{6}{33}\times\frac{5}{32} \\ =\frac{5}{176} \end{gathered}[/tex]

Hence the answer is

[tex]\frac{5}{176}[/tex]