Question

Consider the random experiment of tossing a coin three times. Let S be the collection of all outcomes of this experiment. List the elements of S, using H for head and T for tail.

a) {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
b) {HH, HT, TH, TT}
c) {HHH, HHT, THH, THT}
d) {H, T}

Answer 1

The collection of all outcomes when tossing a coin three times is listed as {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}, representing the sample space of the experiment.

Step-by-step explanation:

The question asks us to consider the random experiment of tossing a coin three times and to list the elements of the set S, which is the collection of all outcomes of this experiment. The sample space S for tossing a coin three times includes every possible combination of heads (H) and tails (T) in each of the three tosses. Therefore, the correct collection of outcomes, using H for heads and T for tails, is:

• HHH
• HHT
• HTH
• HTT
• THH
• THT
• TTH
• TTT

The collection of all outcomes when flipping a coin three times can be represented as {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. Each element of the set represents a different outcome based on the result of each coin toss, where H represents heads and T represents tails.

So, the correct option from the choices provided is a) {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.