Question

two coins are tossed. assume that each event is equally likely to occur.
a) use the counting principle to determine the number of sample points in the sample space.
b) construct a tree diagram and list the sample space.
c) determine the probability that no tails are tossed.
d) determine the probability that exactly one tail is tossed.
e) determine the probability that two tails are tossed.
f) determine the probability that at least one tail is tossed.

a) there is/are 4 sample point(s) in the sample space.
b) construct a tree diagram. choose the correct answer below.
○ a.
○ b.
○ c.
○ d.

Explanation:

Step1: Analyze the tree diagram for two - coin toss

When two coins are tossed, for the first coin (either heads \(H\) or tails \(T\)), and for each outcome of the first coin, the second coin also has two outcomes (\(H\) or \(T\)).

Step2: Check the structure of the tree diagram

The correct tree diagram should start with the first coin toss (either \(H\) or \(T\) as the first - level branches). For each of these branches (say the first coin is \(H\)), the second - level branches should be \(H\) and \(T\) (outcomes of the second coin toss), and the same for the case when the first coin is \(T\).

Answer:

B.