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joint frequency table which summarizes voting trends in the most recent Presidential election

1) Suppose a deck of 10 cards each with a different digit from 0-9 are shuffled and a card from the top of the deck is drawn. Find the following probabilities.
a) That the outcome is odd.
b) That the outcome is prime (2, 3, 5 and 7).
c) That the outcome is odd and prime .
d) That the outcome is odd or prime .
e) That the outcome is prime given that it is odd.
f) That the outcome is neither odd nor prime.

2) Consider the following joint frequency table which summarizes voting trends in the most recent Presidential election.
PARTY AFFILIATION
Democratic Republican Independent TOTAL
VOTED IN 2010
Voted 530 500 470 1500
Didnâ??t Vote 170 174 156 500
TOTAL 700 674 626 1000
a) Convert the table above to a joint probability table.

Use your table in part a) to find the following probabilities.
b) That a survey subject is registered Independent.
c) That a survey subject voted in the 2008 election.
d) That a survey subject is registered Independent and that she or he voted in the 2008 election.
e) That a survey subject is registered Independent or that she or he voted in the 2008 election.
f) Suppose it is known that a survey subject is registered Independent. What is the probability that she or he voted in the 2008 election.
g) What is the probability that two randomly selected survey subjectsâ?? voter registration is Independent. (Hint: This is an â??andâ? probability. Assume independence.

Solution Preview

1.
a) there are 5 odd numbers among the 10 possible values {0,1,2,3,4,5,6,7,8,9}, the probability is 5/10 = 1/2
b) there are 4 favorable outcomes (2,3,5,7) out of 10 total. The probability is 4/10 = 2/5
c) there are 3 odd primes (3,5,7) among the 10 possible outcomes. The probability is 3/10 = 0.3
d) there are 6 numbers that are either odd or prime (or both) among {0,1,2,3,4,5,6,7,8,9}. They are 1,2,3,5,7,9. The probability is 6/10 = 3/5
e) P(prime | odd) = P(prime AND odd) / P(odd) = (3/10)/(5/10) = 3/5. Another way to look at it is, there are 5 odd numbers, three of them are prime.
f) P(not odd AND not prme) = 1 - P(odd OR prime). There are 6 numbers that are either odd or prime: 1,2,3,5,7,9. So, P(odd OR prime) = 6/10, so P(not odd AND not prime) = 1-6/10 = 4/10=0.4
Looking at the problem in another way, there are 4 ...

Solution Summary

Analysis is made on a joint frequency table which summarizes voting trends in the most recent Presidential election.

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