Question

Two fair coins are flipped, one after the other. S 1 = { HH , TT , HT , TH } and S 2 = { one head and one tail , two heads , two tails } . Which of these are equiprobable sample spaces?

S1 only

S2 only

S1 and S2

None of them

Answer 1

A sample space is called an equiprobable space if and only if all the simple events are equally likely to occur.

Now here the random experiment is tossing two fair coins. so the total no. of out comes is : = 4. And the sample space is where, probability of each of the event of the sample is 1/4. So is eqiiprobable.

And, ,where the probability of each sample point is 1/3 which is not equal to 1/4(which is true for the random experiment of tossing two coins) , is not equiporbable sample space.

Note that, is not a sample space but it looks like an event of the sample space ,where is denoting the event space where {TT} is not occured.