Chapter 8.6, Problem 27E

To determine

To find: the probability for the experiment of drawing two marbles at random (without replacement ) form a bag containing one green, two yellow , and three red marbles.

Answer to Problem 27E

The probability of this event is $\frac{1}{5}$ .

Explanation of Solution

Given information: When both marbles are red.

Formula used:

If an event has n(E) equally likely outcomes and its sample space S has n(S) equally likely outcomes, then the probability of event is given by,

  $P(E)=\frac{n(E)}{n(S)}.$

Formula for the number of combinations of n numbers taken r numbers at a time is,

  $n(S){=}_n{C}_r.$

Calculation:

There are ${}_6{C}_2=\frac{6\times 5}{2\times 1}=15,$ different ways to choose two marbles from this bag of 6 marbles.

So, n(S) =15.

There are ${}_3{C}_2=\frac{3\times 2}{2\times 1}=3,$ different ways to choose two of the three red marbles.

So, n (E) = 3.

Therefore, the probability of this event,

  $P(E)=\frac{n(E)}{n(S)}=\frac{3}{15}=\frac{1}{5}.$