Event A: Alternating tail and head (with either coming first) 1/4
Event B: No tails on the first two tosses 3/8
Event C: A tail on both the first and the last tosses 3/8
Let's analyze each event based on the given outcomes:
Outcomes: HHT, HHH, THH, HTH, HTT, TTT, TTH, THT
Event A: Alternating tail and head (with either coming first)
HTH and THT are the outcomes that fit this criterion.
Probability of Event A:
P(A)= 2/8= 1/4
Event B: No tails on the first two tosses
HHH, HTH, and HHT are the outcomes without tails on the first two tosses.
Probability of Event B:
P(B)= 3/8
Event C: A tail on both the first and the last tosses
THH, THT, and TTT are the outcomes with a tail on both the first and the last tosses.
Probability of Event C:
P(C)= 3/8
So, the table would look like this:
Outcomes Probability
---------------------
HHT 1/8
HHH 1/8
THH 1/8
HTH 1/8
HTT 1/8
TTT 1/8
TTH 1/8
THT 1/8
---------------------
Event A: Alternating tail and head (with either coming first) 1/4
Event B: No tails on the first two tosses 3/8
Event C: A tail on both the first and the last tosses 3/8
Question
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The
outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.
Outcomes Probability
HHT HHH THH HTH HTT TTT TTH THT
Event A: Alternating tail and head (with either coming first)
Event B: No tails on the first two tosses
Event C: A tail on both the first and the last tosses