Question

Let T be a random variable giving the number of heads plus the number of tails in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and assign a value to each sample point.

Answer 1

Let's denote H - heads, T - tails.

Sample space S is all possible outcomes of three tosses of a coin.

S = {HHH, THH, HTH, HHT, TTH, THT, HTT, TTT}

Now, T is sum of heads and tails in every element from S. Any element from S consist of 3 events, and every event is either H or T, so for any element from S: T = 3. To show it in detail,

T = {3+0, 2+1, 2+1, 2+1, 1+2, 1+2, 1+2, 3+0} = {3, 3, 3, 3, 3, 3, 3, 3}