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]

Author Credit : The Edifier