Question

Set up several non-uniform sample spaces for the problem of three tosses of a coin

Short answer

The non-uniform sample space are $2t ,1t ,0t$and$0 t ,Atleast 1 t$ ,

Step-by-step solution

Definition of Non-Uniform Sample Space 

Non-Uniform Sample space of any experiment is the set of all possible mutually exclusive events such that each point has different probability to occur

Creation ofsample space for experiment toss of three coins

When three coins are tossed, with each toss there is a possibility of getting head or tail. The sample space is expressed as follows,

$hhh,hht,hth,htt,thh,tht,tth,ttt$

It has 8 events to occur.

Let the event be number of tails when three coins are tossed. The sample space will be and the point has probability$\frac{1}{4}$ $\frac{1}{2}$,and $\frac{1}{4}$respectively and so, it is non-uniform sample space.

The sample space for no tail and at least 1 tail is ,and the point has probability $\frac{1}{4}$and$\frac{3}{4}$ respectively and thus it is non-uniform sample space.