Dependent and independent variables

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Probability is a very important and interesting topic in mathematics. Probability is finding the chances for an event to occur. In a given question there can be more than one event occurring. In such cases it can be checked if one event is dependent or independent from the other. In a question there are two events A and B. If the probability of event ‘A’ occurring affects the probability of event ‘B’ then A and B are dependent event. If the probability of event ‘A’ occurring does not affects the probability of event ‘B’ then A and B are independent event.    

Example 1: In a bag there are 5 marbles. Kelly picks a marble without placing the first one back. Are the events independent or dependent?
Solution: The first event is picking the first marble. The second event is picking the second marble.
Here Kelly picks the second marble without replacing the first marble back in the bag.
So the two events are dependent as second pick is after the first pick of the marble.
Question: Multiple choice question (Pick the correct option.)
The students can choose any field trip between museum and Science Park. Ben picks museum and Sam picks Science Park. What are the events?
a)    Dependent              b) Independent       c) None of these.
Correct answer: option b.
Explanation: The students can choose between any of the two options.
Ben choosing to go to the museum doesn’t affect Sam choosing to go to the Science Park. Hence both the events are independent events. 

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