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. 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 \\( \frac { 1 } { 2 } \\). (simplify your answer.)
e) the probability that two tails are tossed is \\( \square \\). (simplify your answer.)

Explanation:

Step1: Determine sample space size

When two coins are tossed, by counting principle, each coin has 2 outcomes. So total sample points \(n(S)=2\times2 = 4\) (HH, HT, TH, TT).

Step2: Calculate probability for two tails

The event of two tails is \(E = \{TT\}\), so \(n(E)=1\). Probability \(P(E)=\frac{n(E)}{n(S)}\).

Answer:

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