**(D) 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)

A perfect square is chosen

= {16, 25}

**(b)**

A prime number is chosen

= {11, 13, 17, 19, 23}

**(E) 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:

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.

**List the sample space,**

(a)

(a)

*S*.

**(b)**List the elements of

**(**The event

*i*)*P*,

**(**The event

*ii*)*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.)