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 □. (simplify your answer.)

Explanation:

Step1: Determine the sample space

When two coins are tossed, each coin has 2 possible outcomes (H or T). By the counting principle, the total number of sample points is \(2\times2 = 4\). The sample space \(S=\{HH,HT,TH,TT\}\)

Step2: Calculate the probability for part c

The event of no tails (i.e., two heads) is \(E = \{HH\}\). The probability formula is \(P(E)=\frac{n(E)}{n(S)}\), where \(n(E)\) is the number of elements in event \(E\) and \(n(S)\) is the number of elements in sample space \(S\). Here, \(n(E) = 1\) and \(n(S)=4\)

Answer:

\(\frac{1}{4}\)