Probability: Tossing a coin

To find probability of tossing a coin are very interesting and very easy as explained here with the help of different examples.

 
When we flip(toss) a coin there is always a probability to get either ahead or a tail i.e. 50% chance are there for both the events.

Suppose a coin flipped then we get two possible outcomes either a ‘head’ (H) or a ‘tail’ (T), and it is impossible to predict whether the result of a toss will be a ‘head’ or ‘tail.

 Short symbols for used Probability

1. Number of probability = n(p)

2. Expected number of Events = ENE

3. Total Number of Events = TNE

$$n(p)=\frac{ENE}{TNE}$$

Problems based on Probability: Tossing a coin

Find the probability to get Head after tossing 1 Coin?

 
Solution :

 
TNE in tossing one Coin is {H,T}=2
ENE is =1.
$$n(p)=\frac{ENE}{TNE}$$
So, $$n(p)=\frac{2}{4}$$ $$n(p)=\frac{1}{2}$$

Find the probability to get H and T after tossing 2 coins?

Solution :

TNE = {HH, HT, TH, TT}= 4
ENE = {HT, TH} = 2
So, $$n(p)=\frac{2}{4}$$ $$n(p)=\frac{1}{2}$$

 
What is the probability of getting exactly three heads and two tails on five flips of a fair coins?

Solution :

Permutation of 5 letters $$HHHTT=\frac{5!}{3!2!}$$

$$n(p)=\frac{ENE}{TNE}=\frac{\text{Permutation of 5 letters }\{HHHTT\}}{2^5}$$

$$={\displaystyle \frac{\frac{5!}{3!2!}}{2^5}}$$

$$={\displaystyle \frac{\frac{5\times 4\times 3!}{3!2.1}}{2\times 2\times 2\times 2\times 2}}$$

$$n(p)=\frac{5}{16}$$

What is the probability of getting exactly three heads and three tails on six flips of a fair coins?
Answer above question in comments below