Tossing/Throwing Single/One Coin Problems - Probability

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

= 2 {HEAD, TAIL}

⇒ n = 2

Let

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

For Event A

Number of Favorable Choices

= 1 {HEAD}

⇒ 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

= 2 {HEAD, TAIL}

⇒ 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

= 2 {HEAD, TAIL}

⇒ 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 [0]

Practice Problem 3

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

Ans [1]

Author : The Edifier
Page PS3