18 and 19 please! 18. The registered voters of a certain town are 20% Republican

Question

18 and 19 please!

18. The registered voters of a certain town are 20% Republican, 50% Democrat, and 30% Independent. In an election 80% of Republicans vote, 70% of Democrats vote, and 90% of Independents vote. What is the probability that a randomly selected voter actually cast their ballot in the election? 19, City crime records show that 20% of all crimes are violent, while 80% are non-violent. Ninety percent of violent crimes are reported, whereas 70% of non-violent crimes are reported. If a crime in progress is reported to the police, what is the probability that it is violent?

Explanation / Answer

18)
p = 0.20 * 0.80 + 0.50 * 0.70 +0.30 * 0.90
=
0.78

19)
Use of Bayes' theorem
P(violent|reported)
= P(violent and reported)/P(reported)
= 0.20 * 0.9 /(0.20 * 0.90 + 0.80 * 0.70)
= 0.24324324

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