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.
what is the sample space? choose the correct answer below.
a. hh, ht, th, tt
b. h, t
c. h, t, h, t
d. h, t, hh, ht, th, tt
c) the probability that no tails are tossed is \\( \frac { 1 } { 4 } \\). (simplify your answer.)
d) the probability that exactly one tail is tossed is \\( \square \\). (simplify your answer.)

Explanation:

Step1: Determine the sample space

The sample space when two coins are tossed is \(S=\{HH, HT, TH, TT\}\), so there are \(n(S) = 4\) elements.

Step2: Count the number of favorable outcomes for exactly one tail

The events with exactly one tail are \(HT\) and \(TH\). So \(n = 2\).

Step3: Calculate the probability

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\). Here, \(n(A) = 2\) and \(n(S)=4\). So \(P=\frac{2}{4}=\frac{1}{2}\)

Answer:

\(\frac{1}{2}\)