Answer: (1) The sample space is S = {1H, 1T, 2HH, 2HT, 2TH, 2TT, 3H, 3T, 4HH, 4HT, 4TH, 4TT, 5H, 5T, 6HH, 6HT, 6TH, 6TT}
and
(2) The required probability of getting a number 2 and two tails is 0.06.
Step-by-step explanation: Given that a regular die is rolled such that if the number on the die is odd, then a coin is tossed once. If the number on the die is even, the coin is tossed twice.
We are given to
(1). write the sample space for this experiment.
(2). find P(getting a number 2 and two tails).
(1) The sample space S for the given experiment is given by
S = {1H, 1T, 2HH, 2HT, 2TH, 2TT, 3H, 3T, 4HH, 4HT, 4TH, 4TT, 5H, 5T, 6HH, 6HT, 6TH, 6TT}.
(2) Let E be the event of getting a number 2 and two tails.
Then, E = {2, TT} ⇒ n(E) = 1.
Also,
n(S) = 18.
Therefore, the probability of event E is given by
[tex]P(E)=\dfrac{n(E)}{n(S)}=\dfrac{1}{18}=0.06.[/tex]
Thus, the required probability of getting a number 2 and two tails is 0.06.
