Tossing/Throwing/Flipping Single/One Coin Problems :: Probability

No. Problems & Solutions
01.
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.

No. Problems & Solutions
02.
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" be the event of getting a head on throwing the coin.

For Event "A"

Number of Favourable/Favorable Choices = 1 {HEAD}
⇒ mA = 1

∴ Probability of getting a head on throwing the coin

⇒ Probability of occurrence of Event "A" =
No. of Favourable/Favorable Choices for the Event
Total No. 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 (n = 2) possible elementary events, the events of getting a HEAD and getting a TAIL.

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,

The Probability of getting a HEAD ⇒ Probability of occurrence of the elementary event A ⇒ P(A) =
1
2

No. Problems & Solutions
03.
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" be the event of getting both head and tail simultaneously on throwing the coin.

For Event "A"

Number of Favourable/Favorable Choices = 0 {Φ}
⇒ mA = 0

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

⇒ Probability of occurrence of Event "A" =
No. of Favourable/Favorable Choices for the Event
Total No. 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.

No. Problems & Solutions
04.
What are the odds in favour/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" be the event of getting a tail.

For Event "A"

Number of Favourable/Favorable Choices = 1 {TAIL}
⇒ mA = 1

• Odds

No. of UnFavorable Choices = Total No. of possible choices − No. of Favorable choices
⇒ mAc = n − mA
= 2 − 1
= 1

» in favor/favour

Odds in Favour of getting a TAIL
⇒ Odds in Favor/Favour of Event "A" = No. of Favourable Choices : No. of UnFavorable Choices
= m : mAc
= 1 : 1

» against

Odds against getting a TAIL
⇒ Odds against Event "A" = No. of unfavorable Choices : No. of Favourable Choices
= mAc : m
= 1 : 1

No. Problems for Practice
01.
What is the probability of getting tail in a throw of a coin?

Ans [1/2]

02.
What is the probability of getting a head and a tail when we toss an unbiased coin is?

Ans [0]

03.
What is the probability of getting a head or a tail, when we toss a single coin is?

Ans [1]

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