## Understanding Sample Space and Sample Points

In tossing a fair coin, there are only two possible outcomes, a Head (*H*) and a Tail (*T*). If we let *S* be the set of all possible outcomes of this *event*, then, we write the set of possible outcomes as *S* = {*H*,*T*}.

If two fair coins are tossed, then the outcomes can be both heads {*H*,*H*} or both tails {*T*,*T*}. It can also be a head first then a tail {*H,T*}, or a tail first and then a head {*T*,*H*}. So, in tossing two coins, we have the set of possible outcomes *S* = {{*T,T*}, {*T,H*}, {*H,T*}, {*H,H*}}.

As the number of tosses increases, listing gets more difficult. One of the strategies that can be used to remedy this problem is by creating a tree diagram. The following problem is solved using a tree diagram. Notice that it is a three-coin tossing problem in disguise (try replacing *B* with *H* and *G* with *T*). » Read more