Question

Consider an experiment where a coin is flipped 3 times with a sample space {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}, each outcome equally likely.

What represents event A where the first toss is a tail using set notation?
A. {HHT, HTT, HTH, THT}
B. {THH, HTT, TTT}
C. {HTT, TTH, TTT}
D. {THT, TTH, TTT}

Answer 1

Event A, where the first toss is a tail, is correctly represented by set D, which includes {THT, TTH, TTT}, as these are all the outcomes from the sample space where the first coin toss results in a tail.

Step-by-step explanation:

The student's question involves determining the correct set notation for an event A where the first toss results in a tail from a sample space of flipping a coin three times. To identify event A, we should look for outcomes where the first position is a T (tail).

The sample space provided is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. The correct set that represents event A, where the first toss is a tail, includes all sequences starting with the letter T. Thus the correct answer is:

• D. {THT, TTH, TTT}

Options A, B, and C all include sequences that do not start with a T and are thus incorrect for representing event A.