Question

Many American home owners display U.S. flag in their front yard to show their patriotism. In a particular US state 60% of home owners are republicans and 40% are domocrats. A survey indicates that 40% of republicans and 20% of democrats home owners display flags. a. What is the probability that your neighbor is a republican? 5 pts. b. What is the probability that your neighbor is a democrat? 5 pts. c. You notice that your new neighbor hangs a U.S. flag. With this additional information, what is the probability that your neighbor is NOT a republican? 10 pts. d. You notice that your new neighbor hangs a U.S. flag. With this additional information, what is the probability that your neighbor is NOT a democrat? 10 pts.

Answer 1

Answer: a) 0.6, b) 0.4, c) 0.25, d) 0.75

Step-by-step explanation:

Since we have given that

                        Republicans         Domocrats              Total

Display                   0.24                      0.08                   0.32

Don't display          0.36                      0.32                   0.68

Total                        0.6                         0.4                        1

a. What is the probability that your neighbor is a republican?

$P(R)=0.6$

b. What is the probability that your neighbor is a democrat?

$P(D)=0.4$

c.  what is the probability that your neighbor is NOT a republican?

P(not a republican given that display flag) = 1 - P(republican given that display flag)

$=1-\dfrac{P(R\cap F)}{P(F)}\\\\=1-\dfrac{0.24}{0.32}\\\\=1-0.75\\\\=0.25$

d) You notice that your new neighbor hangs a U.S. flag. With this additional information, what is the probability that your neighbor is NOT a democrat?

P(not democrat given that display flag) = 1 - P(democrat given that display flag)

$=1-\dfrac{P(D\cap F)}{P(F)}\\\\=1-\dfrac{0.08}{0.32}\\\\=1-0.25\\\\=0.75$

Hence, a) 0.6, b) 0.4, c) 0.25, d) 0.75