The table above provides information on housing units in some part of the U.S. C

Question

The table above provides information on housing units in some part of the U.S. Consider the following five events: A = the unit has at most four rooms B = the unit has at least two rooms C = the unit has between five and seven rooms inclusive D = the unit has more than seven rooms E = the unit has less than three rooms Determine the number of outcomes (in thousands) that comprise each event given below. not C: not E: A and D: B and E: not D: In the game Roulette, a ball spins on a circular wheel that is' divided into 38 arcs of equal length, numbered 00, 0, 1, 2, ..., 35, 36. The number on the arc on which the ball stops is the outcome of one play of the game. The numbers are also colored as follows: 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36 are red. 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35 are black, 0,00 are green Define the following events: {Outcome is an even number (0 and 00 are considered neither odd nor even)} {Outcome is a red number} Outcome is a green number} {Outcome is a low number (1-18)} Find the following probabilities: P(D) = P(B union D) = P(A intersection B intersection D) = Real estate ads suggest that 51 % of homes for sale have garages, 43 % have swimming pools, and 7 % have both features. What is the probability that a home for sale has a pool or a garage? % neither a pool nor a garage? % a pool but no garage? %

Explanation / Answer

1Q:

Total number of units: 47+140+1170+2350+2450+2130+1370+1560=11217

1)

Number of outcomes in C are 2450+2130+1370 = 5950

By the complement rule, we have

not C = 11217 - 5950 = 5267

2)

Number of outcomes in E are 47+140= 187

By the complement rule, we have

not E = 11217 - 187 = 11030

3)

No unit is possible that has at most 4 rooms and greater than 7 rooms. So

A and D = 0

4)

B and E means units has only 2 rooms. So

B and E = 140

5)

Number of outcomes in D are 1560

By the complement rule, we have

not D = 11217 - 1560 = 9657

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