Probability and Relative Risk Handout - 1 Stat 100A/Sanchez...

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1 Stat 100A/Sanchez Probability 1. Probabilities from Tables of Counts The table below contains information for sales of 4 bedroom houses in Auckland City in June, July and August, 2004. Exercise 1 Days on the market Selling price Less than 30 days 30 – 90 days More than 90 days Total Under $300,000 39 31 15 85 $300,000 - $600,000 35 45 4 84 Over $600,000 8 4 0 12 Total 82 80 19 181 Let C be the event that a house sold for under $300,000, D be the event that a house sold for between $300,000 and $600,000 (inclusive), E be the event that a house sold for over $600,000, F be the event that the sale was made in less than 30 days, G be the event that the sale was made in 30 to 90 days (inclusive), and H be the event that the sale was made in more than 90 days. 1. For a sale selected at random from these 181 sales, find the probability that the sale was: (a) under $300,000 _______________________________ (b) made in less than 30 days _______________________________ (c) under $300,000 and made in less than 30 days _______________________________ (d) under $300,000 or made in less than 30 days _______________________________ _______________________________ (e) $300,000 or more _______________________________ _______________________________ 2 2. For a sale selected at random from these 181 sales, find the probability that the sale was: (a) over $600,000 ___________________________ (b) made in 30 to 90 days (inclusive) ___________________________ (c) over $600,000 and made in 30 to 90 days (inclusive) ___________________________ (d) over $600,000 or made in 30 to 90 days (inclusive) ___________________________ (e) over $600,000 and made in more than 90 days ___________________________ (f) over $600,000 or made in more than 90 days ___________________________ (g) made in at least 30 days ___________________________ 3. The following is a student’s answer to Question 1(d). P(C or F) = = = 0.9227 (to 4 d.p.) Describe why this answer is not correct. ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ 4. (a) Consider the event C or G (That is, house sold for under $300,000 or the sale was made in 30 to 90 days (inclusive). Fill in the gaps: P(C or G) = = = P( ) + P( ) – P( )
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3 (b) Consider the event D or H (That is, house sold for between $300,000 and $600,000 inclusive or the sale was made in more than 90 days). Fill in the gaps: P(D or H) = = = P( ) + P( ) – P( ) (c) Fill in the gaps: For any two events A and B P(A or B) = ________ + ________ – ____________ 5. Look at your answer to Question 2(e). (a) Comment on the events E and H. ________________________________________________________________________ ________________________________________________________________________ (b) E and H are called mutually exclusive events or disjoint events. Fill the gap: For any two mutually exclusive events A and B P(A and B) = _________ Discussion Exercise Days on the market Selling price Less than 30 days 30 – 90 days More than 90 days Total Under $300,000 39 31 15 85 $300,000 - $600,000 35 45 4 84 Over $600,000 8 4 0 12 Total 82 80 19 181 For the 181 house sales in the above table, what proportion of the houses that sold for over $600,000 were on the market for less than 30 days? ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ 4 2. Conditional Probability Exercise 2 Days on the market Selling price Less than 30 days 30 – 90 days More than 90 days Total Under $300,000 39 31 15 85 $300,000 - $600,000 35 45 4 84 Over $600,000 8 4 0 12 Total 82 80 19 181 1. For the 181 house sales in the above table: (a) What proportion of the houses that sold for under $300,000 were on the market for less than 30 days?
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