Question

Two unbiased coins are tossed simultaneously. find the probability of getting:

a.two heads

b.one head

c.at least one head

d.at most one head

e.no head

Answer 1

Back to basics - there are 3 possible (mutually exclusive) outcomes 2H,0T; 1H,1T; 0H,2T. That means that the sum of the 3 probabilities add to 1. The probabilities can be calculated using the binomial distribution. The question asks for P{2H,0T} + P{1H,1T} which is not too hard to calculate, but laziness is a virtue!

Here’s the lazy way P{2H,0T} + P{1H,1T} = 1 - P{0H,2T} and so we can get the answer calculating only one binomial probability and doing the subtraction.

The probability of getting 2T is easy to calculate even mentally - so that, and the subtraction from 1 are left for the reader