**Coin tossing probability :**

Coin tossing experiment always plays a key role in probability concept. Whenever we go through the stuff probability in statistics, we will definitely have examples with coin tossing.

When a coin is tossed, there are two possible outcomes.

They are "head and "Tail".

So, the sample space S = {H, T}, n(s) = 2

When two coins are tossed,

total no. of all possible outcomes = 2 x 2 = 4

So, the sample space S = {HH, TT, HT, TH}, n(s) = 4

When three coins are tossed,

total no. of all possible outcomes = 2 x 2 x 2 = 8

So, the sample space is

S = {HHH, TTT, HHT, HTH, THH, TTH, THT, HTT},

n(s) = 8

In this way, we can get sample space when a coin or coins are tossed.

**Note :**

In coin tossing experiment, we can get sample space through tree diagram also.

We can use the formula from classic definition to find probability in coin tossing experiments.

Let A be the event in a random experiment.

Then,

n(A) = Number of possible outcomes for the event A

n(S) = Number of all possible outcomes of the experiment.

Here "S" stands for sample space which is the set contains all possible outcomes of the random experiment.

Then the above formula will become

To have better understanding of the above formula, let us consider the following coin tossing experiment.

A coin is tossed once.

S = { H, T } and n(S) = 2

Let A be the event of getting head.

A = { H } and n(A) = 1

Then,

P(A) = n(A) / n(S) = 1/2

**Problem 1 :**

A coin is twice. What is the probability of head ?

**Solution :**

When two coins are tossed,

total no. of all possible outcomes = 2 x 2 = 4

And we have, we have the following sample space.

S = {HH, TT, HT, TH} and n(S) = 4

Letting A be the event of getting head, we have

A = {HT, TH} and n(A) = 2

By the classical definition of probability,

P(B) = 2/4

P(B) = 0.50 or 50%

**Problem 2 :**

A coin is tossed three times. What is the probability of getting :

(i) 2 heads

(ii) at least 2 heads

**Solution :**

When a coin is tossed three times, first we need enumerate all the elementary events.

This can be done using 'Tree diagram' as shown below :

Hence the elementary events are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

That is,

S = { HHH, HHT, HTH, HTT, THH, THT, TTH, TTT }

Thus the number of elementary events n(s) = 8

**(i) 2 heads :**

Out of these 8 outcomes, 2 heads occur in three cases namely HHT, HTH and THH.

If we denote the occurrence of 2 heads by the event A and if assume that the coin as well as performer of the experiment is unbiased then this assumption ensures that all the eight elementary events are equally likely.

Then by the classical definition of probability, we have

P(A) = n(A) / n(s)

P(A) = 3/8

P(A) 0.375 or 37.5%

**(ii) at least 2 heads :**

Let B denote occurrence of at least 2 heads i.e. 2 heads or 3 heads.

Since 2 heads occur in 3 cases and 3 heads occur in only 1 case, B occurs in 3 + 1 or 4 cases.

By the classical definition of probability,

P(B) = 4/8

P(B) = 0.50 or 50%

**Problem 3 :**

Four coins are tossed once. What is the probability of getting at least 2 tails ?

**Solution :**

When four coins are tossed once,

total no. of all possible outcomes = 2 x 2 x 2 x 2 = 16

And we have, we have the following sample space.

S = {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, TTTH, TTHT, THTT, HTTT, HHTT, TTHH, HTHT, THTH, HTTH, THHT}

and n(S) = 16

Let A be the event of getting at least two tails.

Then A has to include all the events in which there are two tails and more than two tails.

A = {TTTT, TTTH, TTHT, THTT, HTTT, HHTT, TTHH, HTHT, THTH, HTTH, THHT}

and n(A) = 11

By the classical definition of probability,

P(B) = 11/36

After having gone through the stuff given above, we hope that the students would have understood "Coin tossing probability".

Apart from the stuff given above, if you want to know more about "Coin tossing probability", please click here

Apart from the stuff "Coin tossing probability", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**