UPSC Maths Problems Challenge : A Problem A Day! (Day 3)

It has been a really busy day today (and a partially rough and partially sweet one as well) and there was hardly time to recall that it is my birthday today.I am glad so many of my friends and acquaintances made me feel constantly warm and happy and my family was busy behaving like it is somewhat of a festival!But I hardly got time and then again,a part of the day was rough,wherein I have to still decide if to participate in a quiz competition or not and I am particularly frustrated and really tired about virtual and real concepts.

Coming to the professional part of the post,the problem is a direct problem from Probability.When you look at the problem at a glance,it seems like one of the easiest problems in the world but it certainly is not and is tricky in that sense.

(Original Photograph Source)

Today's Problem(15/06/2015)

A fair coin is tossed 8 times. Find the probability that it shows heads at least once.

Question Credit : http://www.m4maths.com

Now,this is one of those problems you could die for!It is a really tricky question because at a glance it makes you feel like,oh write the outcomes,count the numbers,divide by the total number of possible outcomes.But at least pay attention to the phrase 'at least' within the problem!

Firstly,according to the binomial theorem,we need to find out the probability of getting no heads.

Probability of getting no heads = P (TTTTTTTT) = (1/2)^8 = 1/256

Probability of getting at least one head = 1 - P(No heads) = 1 - 1/256 = 255/256= 0.99609