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

\[n(p) = {ENE\over TNE}\]

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.
\[n(p) = {ENE\over TNE}\]
So, \[n(p) = {2\over 4}\] \[n(p) = {1\over 2}\]

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

Solution :

TNE = {HH, HT, TH, TT}= 4
ENE = {HT, TH} = 2
So, \[n(p) = {2\over 4}\] \[n(p) = {1\over 2}\]

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

Solution :

Permutation of 5 letters \[{HHHTT} = {5!\over 3! 2!}\]

\[n(p) = {ENE\over TNE}={{\text{Permutation of 5 letters } \{HHHTT\}}\over{2^5}}\]

\[ ={\dfrac{5!\over 3! 2!}{2^5}}\]

\[ ={\dfrac{5\times 4\times 3!\over 3! 2.1}{2\times 2\times 2\times 2\times 2}}\]

\[n(p) = {5\over 16}\]

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