Kibiie L.

asked • 04/20/21

Probability in finite math

  1. In a certain congressional district, it is known that 60% of the registered voters classify themselves as conservatives. If ten registered voters are selected at random from this district, what is the probability that six of them will be conservatives? (Round your answer to four decimal places)
  2. A psychology quiz consists of ten true-or-false questions. If a student knows the correct answer to six of the questions but determines the answers to the remaining questions by flipping a coin, what is the probability that she will obtain a score of at least 70%? (Round your answer to three decimal places.) 
  3. In a survey of 1147 small-business owners, the following question was posed: Would you recommend working with a significant other? Fifty-three percent of those polled answered in the affirmative, whereas 47% answered in the negative. Assuming that this result reflects the view of all small-business owners, what is the probability that at least 8 out of 10 small-business owners selected at random will opine that it would be unwise to work with the significant other? (Round your answer to four decimal places.) 

Beth B.

#2 There are 10 T/F questions and we know that the student gets 6 of the 10 correct, so she will score at least a 60%. The other 4 questions: 50% chance to get it correct 50% chance to get it correct 50% chance to get it correct 50% chance to get it correct Chance of getting a 100% 0.5 x 0.5 x 0.5 x 0.5 or (0.5^4) = 0.0625 or 6.25% Chance of getting a 90% or missing 1 of the 4 remaining questions 0.5 x 0.5 x 0.5 = 0.5^3 = 0.125 or 12.5% Chance of getting an 80% or missing 2 of the 4 remaining questions 0.5 x 0.5 = 0.25 or 25% Chance of getting a 70% or missing 3 of the 4 remaining questions 0.5 or 50% So, lets multiply those 4 probabilities together to get the overall chance that she scores a 70% or better 0.0625 x 0.125 x 0.25 x 0.5 = 0.001 or 0.1%
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04/26/21

Beth B.

#3 47% of small business owners in the sample believe that it is not a good idea to work with a significant other. If is this reflects the view of all small business owners, what is the probability that 8 out of 10 believe that it is unwise to work with a significant other? 1: 53% (affirmative) 2: 53% (affirmative) 3: 47% (negative) 4: 47% (negative) 5: 47% (negative) 6: 47% (negative) 7: 47% (negative) 8: 47% (negative) 9: 47% (negative) 10: 47% (negative) .53 x .53 x .47^8 = 0.07%
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04/26/21

1 Expert Answer

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Beth B. answered • 04/26/21

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So, in the 1st question, each of the 10 voters that are selected randomly are each an individual/independent event.


Event/voter 1 = 60% chance of being conservative

Event/voter 2 = 60% chance of being conservative

Event/voter 3 = 60% chance of being conservative

Event/voter 4 = 60% chance of being conservative

Event/voter 5 = 60% chance of being conservative

Event/voter 6 = 60% chance of being conservative

Event/voter 7 = 40% chance of being non-conservative

Event/voter 8 = 40% chance of being non-conservative

Event/voter 9 = 40% chance of being non-conservative

Event/voter 10 = 40% chance of being non-conservative


Note: The order makes no difference here,


0.6 x 0.6 x 0.6 x 0.6 x 0.6 x 0.6 x 0.4 x 0.4 x 0.4 x 0.4

(0.6)^6 x (0.4)^4

0.0012, so 12 out of 10000, or 0.12% chance

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Kibiie L.

It saids that it was wrong
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04/26/21

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