
One cool evening, Arya discovered a hidden Enchanted Garden. Rumors whispered of a magic fountain that granted a single wish—if the right path was chosen among four mysterious routes. Join her as she embarks on an adventure where every choice is a lesson in probability!
Similarly to how, Arya has been presented multiple paths to choose. In probability, the Sample Space is the set of all possible outcomes.
Here, the sample space for Arya is
S = {Gold, Wisdom, Danger,Peace}
n(S) = 4









As Arya thinks about her preferred/favourable path, an Event is any subset of the sample space consisting of Favourable Outcomes.
If Arya's wish is for Peace, then the event is
F = {Peace}
Q. What would be the event if Arya wants to avoid the Danger path?
Probability
Now to find chance for an event, we find probability of that event. Probability is defined as

Examples
Q. If Arya wants to choose the path of Wisdom, what is her chance of choosing the correct path?
Ans. Let W : Arya chooses path of Wisdom
W = {Wisdom}
n(W) = 1
Now, to find probability of choosing Wisdom path
P(W) = n(W) / n(S)
P(W) = 1/4
Q. What is the probability of Arya avoiding the path of Danger?
Can Arya choose multiple paths?
No, Events that can not happen simultaneously are called Mutually Exclusive Events. In Arya's journey, if she chooses Path of Gold then she can not choose Path of Wisdom.
Are there any hidden paths in the forest or do the four paths make up all the choices to be made by Arya?
No, there are no hidden paths, the four paths cover all possible choices. Such events which make up the whole sample space are called as Exhaustive Events.
Arya holds a magical compass that points away from Danger. As, Arya chooses to avoid the Path of Danger, the compass chooses all the outcomes/paths other than the Path of Danger i.e. all the paths opposite to the Path of Danger.
Such an event that consists of all outcomes not in the event is called as Complement of an Event.
Eg. Let D: Arya chooses the Path of Danger
then D' : Arya does not choose the Path of Danger
P(D) = 1/4
P(D') = 1 - P(D)
= 1 - 1/4
P(D') = 3/4
After choosing her path, Arya is facing another dilemma either she can enter the Hidden temple or go on about her initial path. The choices and consequences, she faces do not depend on each other.
Sometimes events do not depend on each other and have independent outcomes, such events are called Independent Events.
We find the joint probability of such events by simply multiplying the respective probabilities.
Eg. For instance, Arya picks a path with a probability of 1/4 and in her journey finds a hidden temple with chance of 1/2 . What is the probability of both happening?
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One cool evening, Arya discovered a hidden Enchanted Garden. Rumors whispered of a magic fountain that granted a single wish—if the right path was chosen among four mysterious routes. Join her as she embarks on an adventure where every choice is a lesson in probability!
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