SOLUTION: MAT 145: Topics In Contemporary Math More Probability 2) A poll was conducted among 250 residents of a certain city regarding tougher guncontrol laws. Own o

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Question 1191734: MAT 145: Topics In Contemporary Math

More Probability
2) A poll was conducted among 250 residents of a certain city regarding tougher guncontrol laws.
Own only a
handgun
Own only a
rifle
Own a
handgun and
a rifle
Own neither Total
Favor
tougher
control laws
0 12 0 138 150
Oppose
tougher laws
58 5 25 0 88
No opinion 0 0 0 12 12
Total 58 17 25 150 250
If one of the participants in this poll is selected at random, what is the probability that they:
a) Favors tougher gun control laws?
b) Owns a handgun only?
c) Owns a handgun?
d) Favors tougher gun control laws and owns a handgun?
e) Opposes tougher gun control laws and does not own a handgun?
f) they own a rifle given they favor tougher gun control laws?
g) favor tougher gun control laws given they own a rifle?
Answer by CPhill(2189)   (Show Source): You can put this solution on YOUR website!
Here's how to calculate the probabilities:
* **Total participants:** 250
* **a) Favors tougher gun control laws:**
* Number who favor tougher laws: 150
* Probability: 150 / 250 = 0.6 or 60%
* **b) Owns a handgun only:**
* Number who own a handgun only: 58
* Probability: 58 / 250 = 0.232 or 23.2%
* **c) Owns a handgun:**
* Number who own a handgun (handgun only + handgun and rifle): 58 + 0 = 58
* Probability: 58 / 250 = 0.232 or 23.2%
* **d) Favors tougher gun control laws and owns a handgun:**
* Number who favor and own a handgun: 0
* Probability: 0 / 250 = 0
* **e) Opposes tougher gun control laws and does not own a handgun:**
* Number who oppose and don't own a handgun: 5 + 25 + 0 = 30 (Rifle only + Handgun and Rifle + Owns neither)
* Probability: 30 / 250 = 0.12 or 12%
* **f) Owns a rifle given they favor tougher gun control laws:**
* Number who own a rifle and favor tougher laws: 12
* Number who favor tougher laws: 150
* Conditional Probability: 12 / 150 = 0.08 or 8%
* **g) Favors tougher gun control laws given they own a rifle:**
* Number who own a rifle and favor tougher laws: 12
* Number who own a rifle: 12 + 5 + 25 = 42
* Conditional Probability: 12 / 42 ≈ 0.286 or 28.6%
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