20% of people vote for party A while the rest vote for party B. Of those who vot
ID: 3172603 • Letter: 2
Question
20% of people vote for party A while the rest vote for party B. Of those who vote for party A, 70% are concerned about the environment. Of those who vote for party B, 60% are concerned about the environment. Suppose we randomly choose someone from the population.
a) Find the probability that this person cares about the environment.
b) Given that the person cares about the environment, find the probability that he votes for party A.
c) Given that the person votes for party A, what is the probability he cares about the environment?
d) What is the probability that the person doesn’t care about the environment?
e) Suppose I keep randomly drawing people until I get someone who votes for party A, what is the probability it takes me 3 draws till that happens?
f) Write the R command needed to get the numeric answer to e.
g) What is the expected number of draws I need to make to get someone who votes party A?
h) What is the probability that it takes me 8 draws to get 3 people who vote for party A?
i) Write the R command I need to use to get the numeric answer to h.
j) What is the expected number of draws needed to get 3 people who vote for party A?
k) If I draw 20 people, what is the probability of getting 5 people who vote for party A?
l) Write the R command to get answer to k.
m) If I draw 20 people, what is the probability of getting less than 5 people who vote for party A? Also, write the R command to get this answer.
n) If I draw 20 people, what is the expected number of party A voters I will get?
o) If I draw 10 people, what is the expected number of eco-friendly people I will get?
Explanation / Answer
probability that person cares about environmen = 0.2*0.7 +0.8*0.6 =0.62
B) given that people care for environmen probability that he votes for party A.
P(A/Env) = 0.2*0.7/0.62 =0.2258
C) its clearly given in question 70% = 0.7
D)
P(Doesn't care about env) = 1- P(care about env) = 1-0.62 =0.38
e) 0.8*0.8*0.2 =0.128
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