INDEPENDENT EVENTS

Definition Of Independent Events

Independent events are events where the outcome of one event does not affect the outcome of the other events.

Video Examples: Independent Events 2
 

Example of Independent Events

Tossing a coin and rolling a number cube are independent events

Solved Example on Independent Events

Ques: Which of the following are independent events?
1. Spinning a number 6 and then spinning a number 5 on the same spinner. 
2. Picking a marble from a jar, then picking another marble after replacing the first one.
3. Picking a red marble from one jar and picking a red ball from another jar.

Choices:

A. 1 and 2 
B. 2 and 3 
C. 1 and 3
D. 1, 2, and 3 
Correct Answer: D

Solution:

Step 1: In (1), the event of spinning a number does not affect the event of spinning another number with the same spinner. 
Step 2: So, the two events are independent.
Step 3: In (2), since a marble picked is replaced before picking another marble, the number of marbles in the jar is not affected.
Step 4: So, picking a marble and then another marble after replacing the first one are independent events.
Step 5: In (3), picking marbles from two different jars are two independent events, as one does not affect the occurrence of other.
Step 6: So, all three events listed are independent.