Write the sample space S and nS for the following experiment

Write the sample space S and n(S) for the following experiment. Then write the given events in set notation and give the probability for the event occurring:

One jar contains four balls labeled 1,2,3,4 and a second jar contains five balls labeled 1,2,3,4,5. An experiment consists of taking one ball from the first jar and then taking a ball from the second jar.

a) The number of the first ball is even
b) the number on the second ball is even
c) the sum of the numbers on the two balls is 5
d) the sum of the numbers on the two balls is 1

Solution

Sample space = {(1,1), (1,2), (1,3),(1,4),(1,5)               
(2,1),(2,2),(2,3), (2,4),(2,5)      
(3,1),(3,2), (3,3),(3,4),(3,5)      
(4,1),(4,2),(4,3) ,(4,4),(4,5)      
(5,1),(5,2),(5,3), (5,4),(5,5) } = n(S) = 25

a) The number of the first ball is even
= { (2,1),(2,2),(2,3),(2,4),(2,5)  
(4,1),(4,2),(4,3),(4,4),(4,5) } = 10
P( first ball is even ) = 10/25 = 2/5

b) The number on the second ball is even
= { (1,2), (1,4) , (2,2) (2,4) (3,2) (3,4) (4,2) (4,4) (5,2) (5,4) }

P( second is even) = 10/25 = 2/5

c) The sum of the numbers on the two balls is 5
= { (1,4), (2,3) , (3,2) , (4,1) } = 4/25

d) The sum of the numbers on the two balls is 1
= No such event is possible