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

Explanation:

Step1: Determine sample space using counting principle

When tossing a coin, there are 2 possible outcomes (H or T). For two - coin tosses, by the counting principle \(n = 2\times2=4\)

Step2: Analyze sample space

The sample space for two - coin tosses is all possible combinations of the outcomes of the first and second coin tosses.
The first coin can be H or T, and for each of these, the second coin can be H or T.
If the first coin is H, the second can be H (HH) or T (HT). If the first coin is T, the second can be H (TH) or T (TT)

Answer:

A. HH, HT, TH, TT