# Problem 1

Write all the elementary events in an experiment of tossing an unbiased coin.

# Solution

In the experiment of tossing an unbiased coin, there are two possible elementary events:
• The event of getting a HEAD
• The event of getting a TAIL.

# Problem 2

In a single toss of a fair coin, find the probability of getting head.
(Or) If a coin is tossed, what is the chance of a head?

# Solution

In the experiment of tossing a coin,

Total Number of Possible Choices

⇒ n = 2

Let

A : the event of getting a head on throwing the coin.

## For Event A

Number of Favorable Choices

⇒ mA = 1

Probability of getting a head on throwing the coin

⇒ Probability of occurrence of Event A

=
 Number of Favorable Choices for the Event Total Number of Possible Choices for the Experiment
⇒ P(A) =
 mA n
=
 1 2

## Alternative

In an experiment with n elementary events all of which are equally likely, mutually exclusive and exhaustive, the probability of occurrence of each elementary event is
 1 n
.

In the experiment of tossing a coin,

There are two possible elementary events, the events of getting a HEAD and getting a TAIL.

⇒ n =2

These elementary events are

• Mutually exclusive

since only one of them can appear at a time

• Equally likely

since we can expect any one of them to appear and

• Exhaustive

since these are the only two possibilities in the experiment.

If A is the event of getting a HEAD,

## For Event A

The Probability of getting a HEAD

⇒ Probability of occurrence of the elementary event A

⇒ P(A) =
 1 2

# Problem 3

If a perfect coin is tossed, the probability of getting both head and tail simultaneously is __

# Solution

## simultaneously

• at the same instant

In the experiment of tossing a coin,

Total Number of Possible Choices

⇒ n = 2

Let

A : the event of getting both head and tail simultaneously on throwing the coin.

## For Event A

Number of Favorable Choices

= 0 {Φ}

⇒ mA = 0

Probability of getting both head and tail simultaneously on throwing the coin

⇒ Probability of occurrence of Event A

=
 Number of Favorable Choices for the Event Total Number of Possible Choices for the Experiment
⇒ P(A) =
 mA n
=
 0 2
= 0

## Impossible Event

The event of getting a head and tail simultaneously is impossible since only one of these can appear at a time on throwing a coin.

The probability of an impossible event is zero.

# Problem 4

What are the odds in favor of and against getting a tail on tossing a coin.

# Solution

In the experiment of tossing a coin,

Total Number of Possible Choices

⇒ n = 2

Let

A : the event of getting a tail.

## For Event A

Number of Favorable Choices

= 1 {TAIL}

⇒ mA = 1

Probability of getting both head and tail simultaneously on throwing the coin

⇒ Probability of occurrence of Event A

=
 Number of Favorable Choices for the Event Total Number of Possible Choices for the Experiment
⇒ P(A) =
 mA n
=
 0 2
= 0

## Odds

Number of Unfavorable Choices

= Total Number of possible choices − Number of Favorable choices

 ⇒ mAc = n − mA = 2 − 1 = 1

## in favor

Odds in Favor of getting a TAIL

⇒ Odds in Favor of Event A

= Number of Favorable Choices : Number of Unfavorable Choices

= mA : mAc

= 1 : 1

## against

Odds against getting a TAIL

⇒ Odds against Event A

= Number of Unfavorable Choices : Number of Favorable Choices

= mAc : mA

= 1 : 1

# Practice Problem 1

What is the probability of getting tail in a throw of a coin?

Ans [1/2]

# Practice Problem 2

What is the probability of getting a head and a tail when we toss an unbiased coin is?

Ans 

# Practice Problem 3

What is the probability of getting a head or a tail, when we toss a single coin is?

Ans