Consider two urns of balls: the first contains 5 different red balls numbered fr
ID: 3352144 • Letter: C
Question
Consider two urns of balls: the first contains 5 different red balls numbered from 1 to 5 and the second contains 4 different blue balls numbered from 1 to 4. You are asked to pick one ball from the first urn (i.e., the one with red balls) and one ball from the second urn (i.e. the one with blue balls). Each outcome has the form (r, b), where r denotes the number on the red ball and b denotes the number on the blue ball. For example (2,3) corresponds to picking the red ball with number 2 and the blue ball with number 3. (a) Write the sample space S. (b) Write the set representing the event A-(b is either 1 or a prime number). (c) Write the set representing the event A2 -r is an even number and b is an odd number) d) Write the set representing the event As (the product of r and b is an even number (e) Write the set representing the event Bthe sum of r and b is greater than or equal to 5) () Write the set representing the event B2-rand b are equal g) Write the set representing the event Bs-r is an odd number and b is either 1 or 3) For each pair of sets Ai and B, A2 and B2, As and B3, identify whether the pair of sets is either mutually exclusive or collectively exhaustive or both.Explanation / Answer
A) S = {(1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4), (5,1), (5,2), (5,3), (5,4)}
B) A1 = {(1,1), (2,1), (3,1), (4,1), (5,1), (1,2), (2,2), (3,2), (4,2), (5,2), (1,3),(2,3),(3,3),(4,3),(5,3)}
C) A2 = {(2,1), (2,3), (4,1),(4,3)}
D) A3 = {(2,2), (4,2), (4,2), (4,4)}
E) B1 = {(1,4), (2,3), (2,4), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4), (5,1), (5,2), (5,3), (5,4)}
F) B2 = {(1,1), (2,2), (3,3), (4,4)}
G) B3 = {(1,1), (1,3), (3,1), (3,3), (5,1), (5,3)}
H) A1 and B1 - collectively exhaustive
A2 and B2 - mutually exclusive
A3 and B3 - mutually exclusive
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