# Define following with examples: 1. Equaly likely events, 2. Mutually Exclusive event, 3. Exhaustive event, 4. Sure event, 5. Impossible event.

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by AlekhyaSistu
can you please define sample space also

2015-04-01T20:05:01+05:30
Equally likely:something that have equal chance of occurring Eg:India and Pakistan winning the toss Sure:something that must occur Eg:Gandhi ji birthday is on 2 October Impossible :something that cannot happen Eg: a ranker to fail in exams Mutually Exhaustive event:something that would occur with a great chance Eg:an average student to get above80 Exhaustive:something that would occur with less chance Eg:a failure to get good marks
can you please define sample space in simple words
2015-04-01T20:49:55+05:30

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4. Sure event :  the probability of the event = 1.
Sun rises in the East tomorrow and the day after.
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5. Impossible event.
The probability the event happening is zero.  The event will never happen.
A person being 5 meters tall and 6 meters tall at the same time.
Both teams winning the match.  Moon stops revolving around the Earth in the next day.
Electrons stop running on electrical wire when there is voltage on the wire.
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3.  Exhaustive events:
We list all possible outcomes of an event.  Happening or occurring of all these  outcomes will be called the exhaustive events.
Suppose A coin is tossed.  The exhaustive events are : occurring of a Head and the occurring of a Tail.
Suppose a die is rolled.  The showing up of 1, 2, 3, 4, 5, and 6 are the exhaustive events.  This set covers all possibilities that can happen.
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2. Mutually exclusive event:
When a coin is tossed it shows up either a Head or a Tail.  If Head shows up , then the event of Tail showing up cannot happen.  Similarly, When a tail shows up, the event of a head showing up is not possible.
So those events which do not happen together, and there is no possibility of their common occurrence are called mutually exclusive events.
If you wear shoes, you cannot wear sandals on your feet.  So wearing of shoes and wearing of sandals are mutually exclusive events.
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1.  Equally likely events:
When a fair, unbiased and perfect coin is tossed up,  the showing up of a head or a tail are equally likely.  Either could happen with equal probability.
Those events / outcomes which have equal probability (of happening) are called equally likely events.
When a die is tossed up,  the faces with numbers 1, 2, 3, 4, 5, or 6 are all equally likely to show up.  We assume it is a fair and unbiased die.