You flip a fair coin 5 times. What is the probability that the first flip results in heads or the fifth flip results in heads?
a) 1/4
b) 1/2
c) 3/4
d) 1
Solution: 2014 Fall Midterm - 14
Author: Michiel SmidQuestion
You flip a fair coin 5 times. What is the probability that the first flip results in heads or the
fifth flip results in heads?
(a)
1
(b)
3/4
(c)
1/4
(d)
1/2
Solution
$Pr(A)$ = probability of first flip being heads = $1/2$
$Pr(B)$ = probability of fifth flip being heads = $1/2$
$Pr(A \cap B)$ = probability of both the first and fifth flip being heads = $(1/2) \cdot (1/2) = 1/4$
$|A \cup B| = |A|+|B|-|A \cap B|$
$|A \cup B| = \frac{1}{2}+\frac{1}{2}-\frac{1}{4}$
$|A \cup B| = \frac{3}{4}$