Probability is so important. It is an expectation of the happening of some event. In our daily life, we often predict the outcome of several events and hear phrases like “probably it will rain today”. The rolling of coin is one of the most easiest way to learn probability.
In this blog, We will see how to easily and quickly calculate the probability of a coin.
Lets understand a few terms first.
Sample Space : It is defined as the set of all possible outcomes of a random experiment associated with it.
Probability of an event E and is written as P(E) and is defined as
P(E) = No of outcomes favorable to E / Total no. of outcomes
When a fair coin is tossed once the sample space is
S = [Head, Tail]
Now the probability of getting a heads is,
P(E) = no of Head in S / total in S
P(E) = 1/2
Simple, eh ?
When a fair coin is thrown twice or two coins are thrown the sample space would have 4 elements
For ease of calculations, we will go with H for heads and T for Tails
S = [ HH, HT, TH, TT]
Now the probability of getting atleast one Tail (T) would be,
P(E) = no of elements in S atleast one is Tail / Total outcomes.
P(E) = 3 / 4
When a fair coin is thrown thrice or three coins are thrown the sample space would have 8 elements
S = [ HHH, HTH, THH, TTH, HHT, HTT, THT, TTT]
In general if , a coin is thrown “n” times the sample space has “2^n” elements.
Just remember these sample spaces and any question on coins can be easily solved.
Thank you for reading.
