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Find the probability

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A box contains six (6) red balls, nine (9) white balls, and five (5) blue balls. A ball is selected and then replaced. Then, a second ball is selected.

1. both balls are white

2. the first ball is red and the second is white.

3. both balls are blue

Mar 9th, 2015

9-13: This is sampling with replacement, so the probability of drawing any particular color does not change from draw to draw. 
The total number of balls is 20. 

9) The probability of drawing white is 9/20. Since these are independent draws, the probability of both draws being white is 9/20 * 9/20 = 81/400. 

10) P(red) = 6/20; P(white) = 9/20; total = 6/20 * 9/20 = 54/400 
11) P(blue) = 5/20; P(blue, blue) = 25/400 
12) P(yellow) = 0; P(blue) = 5/20. P(yellow) * P(blue) = 0 
13 P(not blue) = 15/20; P(not blue)² = 255/400 

14-18: This is sampling without replacement. The odds change for the second draw because the numerator may change and the denominator will change. 

14) P(1st=purple) = 5/10; P(2nd=orange) = 2/9; P(1st=purple) * P(2nd=orange) = 10/90 = 1/9 
15) P(1st=purple) = 5/10; P(2nd=blue) = 0; P(1st=purple) * P(2nd=blue) = 0; 
16) P(1st=orange) = 2/10; P(2nd=purple) = 5/9; P(1st=orange) * P(2nd=purple) = 2/10 * 5/9 = 10/90 = 1/9 
17) P(1st=green) = 3/10; P(2nd=purple) = 5/9; P(1st=green) * P(2nd=purple) = 3/10 * 5/9 = 15/90 
18) P(1st=orange) = 2/10; P(2nd=orange) = 1/9; P(1st=orange) * P(2nd=orange) = 2/10 * 1/9 = 2/90 

Notice how the numerator changed for the second draw of "orange" in #18 

19) P(A) = 3/6 (three regions are odd-numbered out of six total) 
20) P(B) = 1/6 (one region is numbered 5 out of six total) 
21) P(A and B) = 1/6 ("and" means the spinner lands in a spot qualifying for membership in both sets -- both odd, and numbered "5". In other words, the set intersection. Only 1 of the 6 spaces qualifies for membership in both sets.) 
22) P(A or B) = 1/2 ("or" means the spinner lands in a spot qualifying for membership in either set, or both. In other words, the set union.)

answer both balls are white

best my answer :)

Mar 9th, 2015

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