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.

Examples of Independent Events

• Tossing a coin and rolling a number cube are independent events.

Solved Example on Independent Events

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

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.

Related Terms for Independent Events

• Event
• Outcome

Additional Links for Independent Events

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