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.

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 $\frac{1}{4}$. (simplify your answer.)
f) the probability that at least one tail is tossed is $square$. (simplify your answer.)

Explanation:

Step1: Find the total number of sample points

From part a), using the counting principle, when two coins are tossed, the total number of sample points \(n(S)=4\) (from \(2\times2\) as each coin has 2 outcomes).

Step2: Define the event for at - least one tail

The event of getting at least one tail is the complement of the event of getting no tails. Let \(A\) be the event of getting at least one tail and \(B\) be the event of getting no tails. We know \(P(B)=\frac{1}{4}\) (from part c)).
Using the formula \(P(A)=1 - P(B)\)

$$P(A)=1-\frac{1}{4}$$

Step3: Calculate the probability

$$P(A)=\frac{4 - 1}{4}=\frac{3}{4}$$

Answer:

\(\frac{3}{4}\)