7.2 Events
(A) Elements of a Sample Space which Satisfy Given Condition
When a specific condition is given, we can list the elements of a sample space which satisfy the given condition.
Example 1:
A two-digit number which is not more than 25 is chosen at random. List the elements of the sample space which satisfy each of the following conditions.
(a) A perfect square is chosen.
(b) A prime number is chosen.
Solution:
Sample space
= {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}
(a)
A perfect square is chosen
= {16, 25}
(b)
A prime number is chosen
= {11, 13, 17, 19, 23}
(B) Events for a Sample Space
An event is a set of outcomes which satisfy a specific condition.
Event is a subset is a sample space.
Example 2:
A coin and a die are thrown simultaneously. The events P and Q are defined as follows.
P = Event of obtaining a ‘heads’ from the coin and an odd number from the die.
Q = Event of obtaining a ‘tails’ from the coin and a number more than 2 from the die.
(a) List the sample space, S.
(b) List the elements of
(i) The event P,
(ii) The event Q.
Solution:
(a)
Sample space, S
= { (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6) }
(b)(i)
P = { (H, 1), (H, 3), (H, 5) }
← (Set of outcomes of Event P: obtaining a ‘heads’ from the coin and an odd number from the die.)
(b)(ii)
Q = { (T, 3), (T, 4), (T, 5), (T, 6) }
← (Set of outcomes of Event Q: obtaining a ‘tails’ from the coin and a number more than 2 from the die.)