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$$P(X \, and \, Y)=P(X)\cdot P(Y\: after\: x)$$ Example What is the probability for you to choose two red cards in a deck of cards? The probability of choosing a red card randomly is: $$P\left ( red \right )=\frac=\frac$$ The probability of choosing a second red card from the deck is now: $$P\left ( red \right )=\frac$$ The probability: $$P\left ( 2\,red \right )=\frac\cdot \frac=\frac$$ Two events are mutually exclusive when two events cannot happen at the same time.
So, the total events are ‘2’ (raining or not raining).
And, the probability of raining is 1/2So, Probability of an event happening = Concerned Events / Total Events Probability of an event happening is denoted by P(E)Probability of an event not happening is denoted by P(Ē). If ‘And’ event is given then we multiply or count events together.2.
Example What is the probability to get a 6 when you roll a die?
A die has 6 sides, 1 side contain the number 6 that give us 1 wanted outcome in 6 possible outcomes.
Consider this, if it’s cloudy outside then two things can happen.
First, either it will rain or second, it won’t rain.What is the probability that the wheel stops at red or pink?P(red or pink)=P(red) P(pink) $$P\left (red \right )=\frac=\frac$$ $$P\left (pink \right )=\frac$$ $$P\left ( red\, or\, pink \right )=\frac \frac=\frac$$ Inclusive events are events that can happen at the same time.Dependent events: Two events are dependent when the outcome of the first event influences the outcome of the second event.The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.Probability questions are an important part of Quantitative aptitude section of most competitive exams like SBI, IBPS, PO/Clerk, LIC-AAO etc. The probability of an event happening ranges between 0 to 1.These questions are asked frequently so it becomes really relevant to know the right technique of solving these questions. That means the value of probability can never be a negative number or a number greater than 1.$$P(X \, or \, Y)=P(X) P(Y)$$ An example of two mutually exclusive events is a wheel of fortune.Let's say you win a bar of chocolate if you end up in a red or a pink field.$$P(X \, and \, Y)=P(X)\cdot P(Y)$$ To find the probability of an independent event we are using this rule: Example If one has three dice what is the probability of getting three 4s?The probability of getting a 4 on one die is 1/6 The probability of getting 3 4s is: $$P\left ( 4\, and\, 4\, and\, 4 \right )=\frac\cdot \frac\cdot\frac=\frac$$ When the outcome affects the second outcome, which is what we called dependent events.