Events Examples - Word Problems

# Events Examples

Events are the outcomes of a random experiment. When a random experiment is carried out, more than one outcomes are possible, each one of which is known as an event. The set of all the events is known as the sample space of the experiment. There are different types of events who have their own properties. These events are: simple and compound, independent and dependent, mutually exclusive, mutually exhaustive.

## Word problems

Problem 1:

A die is thrown, then what kind of the event will be the event of getting an odd number?

Solution:

The sample space of the throw of a die is $\{1,\ 2,\ 3,\ 4,\ 5,\ 6\}$.

The event of getting an odd number = $\{1,\ 3,\ 5\}$ which is having more than one simple event.

Hence, this is a compound event.
Problem 2:

Given below are few events. Classify them.

a) Stepping on a red square in a room having $20$ red and $20$ white squares.

b) Getting head or tail in tossing a coin.

c) Anin wearing a combination of red top and black jeans today out of $3$ different colors tops and jeans she has.

Solution:

The classification of the events is given here:

a) This is a simple event as the sample space is having only two events, that is, red and white. The event of stepping on to a red square cannot be disintegrated any further.

b) These are mutually exclusive events as they cannot happen together.

Also, they are mutually exhaustive events as they together equals to the whole sample space.

Getting a head or getting tail, separately, are simple events.

c) The event is $\{red\ top,\ blue\ jeans\}$. It can be further disintegrated to simpler events $\{red\ top\}$ and $\{blue jeans\}$. Hence, it is a compound event.
Problem 3:

The probability of having snowfall in London today is $0.3$. What will be the probability that there is no snowfall in London today?

Solution:

To have a snowfall and to not have a snowfall are complementary events. Hence, the probability of not having snowfall is the complement of the probability of having snowfall.

Probability of not having snowfall = $1\ -\ 0.3$ = $0.7$
Problem 4:

There are $2$ red and $6$ green balls in a bag. If two balls are taken out one by one with replacement what is the probability that we get $1$ red and $1$ green ball.

Solution:

These two events are independent of each other.

Probability of getting a red ball, $P(A)$ = $\frac{2}{8}$

Probability of getting a red ball, $P(B)$ = $\frac{6}{8}$

Probability of getting a red and a green ball = $P(A)\ \times\ P(B)$ = $\frac{2}{8}$ $\times$ $\frac{6}{8}$ = $\frac{3}{16}$