Question

A jar contains six blue marbles and five red marbles. Suppose you choose a marble at​ random, and do not replace it. Then you choose a second marble. Find the probability of the following event. Both of the selected marbles are red.

Answer 1

The jar has 6+5=11 marbles.

We have to find the probability of the following event:

1.We pick a marble from a jar that has 11 marbles in total, 5 of them are red

2.We pick a marble from a jar that has now 10 marbles in total, 4 of them are red (because in the previous step we picked a red marble and did not put it back in the jar)

The probability of the first event is:

$P_1=\frac{5}{11}$

The probability of the second event is:

$P_2=\frac{4}{10}=\frac{2}{5}$

The probability of the both events to happen is:

$P=P_1\cdot P_2=\frac{5}{11}\cdot \frac{2}{5}=\frac{2}{11}=0.1818$