Probability Line Examples - Word Problems

# Probability Line Examples

Probability line is a line from 0 to 1 which represents the probability of different events. The events closer are zero are more unlikely to happen than the events closer to one. The zero is marked on the left side of the line and one is marked on the right side of the line. Probability of any event lies between 0 to 1.
The probability line divides the events in five types:

1) Impossible

2)
Unlikely

3)
Even Chances

4)
Likely

5)
Sure Event

## Word Problems

Let us see some examples to understand the concept.
Problem 1:

Represent the given events on a probability line.

a) Getting $2$ in a throw of a dice.

b) Getting an even number in a throw of a dice.

c) Getting a positive number in a throw of a dice.

Solution:

The probabilities can be calculated as given here,

Probability of getting a $2$ = $\frac{1}{6}$

Probability of getting an even number = $\frac{1}{2}$

Probability of getting a positive number = $1$ Problem 2:

Two coins are tossed simultaneously. Represent the given events of this experiment on a probability line.

a) Getting at least one head.

c) Getting one head and one tail

Solution:

Sample space = $\{HH,\ HT,\ TH,\ TT\}$

Given are the probabilities of these events.

Probability of getting one head = $\frac{3}{4}$

Probability of getting two head = $\frac{1}{4}$

Probability of getting one head and one tail= $\frac{2}{4}$ = $\frac{1}{2}$ Problem 3:

A bag has $2$ red, $3$ green and $1$ black ball. Few events have been given below.

a) Getting $2$ red balls when $2$ balls are picked with replacement.

b) Getting $2$ green balls when $2$ balls are picked in random without replacement.

Solution:

Total number of balls = $6$

The probability of getting $2$ red balls with replacement = $\frac{2}{6}$ $\times$ $\frac{2}{6}$ = $\frac{1}{9}$

The probability of getting $2$ green balls without replacement = $\frac{3}{6}$ $\times$ $\frac{2}{5}$ = $\frac{1}{5}$ Problem 4:

Arrange these events on a probability line.

a) Having snowfall in Africa.

b) Finding oasis in Antarctica.

c) The fan in the room is off

Solution:

Having snowfall in Africa and finding an oasis in Antarctica are impossible events.

There are even chances of a fan to be off.

Hence, on the below probability line we can show the events. 