a coin is tossed twice, or until the first "tails" appears, whichever comes first. which of the following is the sample space for this random experiment?
A, S=(H, T)
B. S=(T, HT, HH)
C. S=(T, TT)
To determine the sample space of a random experiment, we need to list all the possible outcomes.
In this case, we have three possible outcomes for each toss: "H" for heads and "T" for tails.
Let's consider each option:
A. S=(H, T): This option represents the possible outcomes of a single coin toss. However, since two tosses are involved, it does not account for the possibility of getting two heads in a row before getting tails.
B. S=(T, HT, HH): This option represents the possible outcomes of two coin tosses or until the first tails appears. It includes the possibility of getting tails on the first toss ("T"), as well as the possibility of getting tails on the second toss after getting heads on the first toss ("HT"). However, it does not account for the possibility of getting two heads in a row before getting tails.
C. S=(T, TT): This option represents the possible outcomes of two coin tosses or until the first tails appears. It includes the possibility of getting tails on the first toss ("T"), as well as the possibility of getting tails on the second toss after getting tails on the first toss ("TT"). However, it does not account for the possibility of getting heads before getting tails.
Therefore, the correct answer is option B. The sample space is S=(T, HT, HH).