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# Example: All the ways you can flip a coin

## Video transcript

find the probability of getting exactly two heads when flipping three coins so let's think about the sample space here let's think about all of the possible outcomes so I could get all heads so on flip one I get a head flip two I get a head flip three I get a head I could get two heads and then a tail I could get heads tail heads or I could get heads tails tails I could get tails heads heads I could get tail heads tails I could get tails tails heads or I could get tails tails and Tails these are all the different ways that I could flip three coins and you can maybe say that this is the first flip the second flip and the third flip now so this right over here is the sample space there's eight possible outcomes let me write this the probability of exactly two heads exactly exactly two heads - I'll say H is therefore short the probability of exactly two heads well what is the size of our sample space I have eight possible outcomes so eight this is possible outcomes or the size of our sample space possible outcomes and how many of those possible outcomes are associated with this event you could call this a compound event because there's more than one outcome that's associated with this well so let's think about exactly exactly two eyes this is three heads so it's not exactly two heads this is exactly two heads right over here this is exactly two heads right over here there's only one head this is exactly two heads this is only one head only one head no heads so you have one to three of the possible outcomes are associated with this event so you have three possible outcomes three outcomes associated with event three outcomes outcomes satisfy satisfy this event or associated with this event so the probability of getting exactly two heads when flipping three coins is three outcomes satisfying this event over eight possible outcomes so it is 3/8