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

8 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 TTH TTT HHH THT HTT THH HHT HTH Event A: A tail on the first toss Event B: Alternating tail and head (with either coming first) Event C: Exactly one head

Answer 1

Solution:

A coin is tossed 3 times.

Event A: A tail on the first toss

This event can be represented by following outcomes:

TTH, TTT, THT and THH

Probability of every outcome is same and this probability is equal to .

Since, outcomes are independent to each other,

Probability of event A is 1/2.

b) Event B: Alternating tail and head (with either coming first)

This event can be represented by following outcomes:

THT and HTH

Pobability of every outcome is same and this probability is equal to .

Since, outcomes are independent to each other,

Probability of event B is 1/4.

c) Event C: Exactly one head

This event can be represented by following outcomes:

HTT, THT and HTT

Probability of every outcome is same and this probability is equal to .

Since, outcomes are independent to each other,

Probability of event A is 3/8.

Please rate the answer. Thank you.