Question

Two red marbles, one white marble and one blue marble are in a bag. Two marbles are selected. Find the sample space of the experiment, then the probability of selecting at least one red marble, and the complement of this event and find its probability.

Answer 1

SOLUTION

The bag contains the following marbles

2 red, 1 white and 1 blue.

(a) Sample space means listing all the possible outcomes, which is done thus:

Since two marbles are usually picked. It is either we pick

2 red marbles or

1 red and 1 white

1 red and 1 blue

1 white and 1 blue.

Hence the sample space is

2 red marbles

1 red and 1 white

1 red and 1 blue

1 white and 1 blue.

(b) The probability of selecting at least one red marble

The probability of selecting at least 1 red marble is

1 - probability of selecting no red marble

$P(at\text{ least one red) = 1 - P(no red)}$

Now from what we have above

2 red marbles or

1 red and 1 white

1 red and 1 blue

1 white and 1 blue

It means that the total sample space is 4, that is 4 possible outcomes.

Not picking red means picking 1 white and 1 blue (that is 1 outcome)

Hence probability of no red is

$P(no\text{ red) = }\frac{1}{4}$

The probability of selecting at least 1 red marble becomes

$\begin{gathered} 1-\frac{1}{4} \\ =\frac{3}{4} \end{gathered}$

The complement of this event that is (the probability of selecting at least 1 red marble is) is the probability of selecting no red marble.

We have gotten that initially as

$\frac{1}{4}$