Question

We are flipping four coins. Outcomes in the sample space are represented by strings of Hs and Ts such as TTHT and HHTT.
a. How many elements are in this sample​ space?
b. Express the event​ "there are more heads than tails​" as a set.
c. What is the probability that there are more heads than tails​?
d. What is the probability that there are an equal number of heads and tails​?

Answer 1

a.
Either you could think of every single combination or just realize that there are four events:
_ _ _ _
For each event, there are 2 possibilities, heads or tails. Therefore, for 4 coins:
\(2\times2\times2\times2\)\(=\)\(2^4\)
There are that many possibilities.
b.
To have more tails than heads, you need to have either 3 heads or 4 heads of all 4 coins. Now you can express that as a set.
c.
Based on part b...
\(P(h>t)=\frac{_4C_3+_4C_4}{2^4}\) as you need to have the combinations it takes to get 3 heads PLUS 4 heads (addition rule of probability) over the combination of all events. Now you can evaluate

d.
You need to have 2 heads and 2 tails
\(P(h=t)=\frac{_4C_2}{2^4}\)
now you can evaluate