Rivalry2

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Original 2026-01-01

Modified 2026-02-28

1 <p>Events in probability can be classified into a variety of categories. A random experiment can only have one sample space (set of all possible outcomes of an experiment), but it can have a wide variety of events. </p>

2 <p>The following is a list of some important probability events. </p>

3 <ul><li>Independent and Dependent Events </li>

4 <li>Impossible and Sure Events </li>

5 <li>Complementary Events </li>

6 <li>Mutually Exclusive Events </li>

7 <li>Exhaustive Events </li>

8 <li>Equally Likely Events</li>

9 </ul><h3>Independent and Dependent Events</h3>

10 <p>In probability,<a>independent events</a>are events whose outcomes are not affected by the outcome of any previous event.</p>

11 <p>For example,<a>tossing a coin</a>is an independent event, because the previous event like getting heads will not affect the next outcome. </p>

12 <p>Dependent events are those events that will depend on the outcome of the previous results.</p>

13 <p>For example, imagine you pick a ball, let’s say Ball A, from a bag containing different colors of balls. When you pick another ball, there won't be Ball A in the bag. That means the probability of not getting Ball A is already determined. </p>

14 <h3>Impossible and Sure Events</h3>

15 <p>An event that will not happen is known as an impossible event. The<a>probability of an impossible event</a>is 0 (zero).</p>

16 <p>For example,<a>rolling a die</a>numbered 7 is an impossible event because a die has numbers only from 1 to 6.</p>

17 <p>On the other hand, a sure event is the one that will happen for sure. The probability of an event that will happen for sure is 1 (one). For example, a sure event is the Sun rising tomorrow. It will happen no matter what (unless we consider extreme cosmic events). </p>

18 <h3>Simple and Compound Events</h3>

19 <p>A simple event is when there is only one specific outcome out of all possible outcomes.</p>

20 <p>For example, when rolling a six-sided die, the sample space (all possible outcomes) is {1, 2, 3, 4, 5, 6}. Getting a 4 on a rolling die refers to just one outcome 4, that is, E = {4}. </p>

21 <p>Whereas, an event that consists of more than one single event from the sample space is called a compound event. For example, getting an<a>odd number</a>on a die is a compound event as the events are E = {1, 3, 5} (<a>multiple</a>events from a single sample space).</p>

22 <h3>Complementary Events</h3>

23 <p>Complementary events are two events in which one of the two can only occur if and only if the other does not exist. The<a>sum</a>of the complementary events is 1 (one).</p>

24 <p>For example, Event A of drawing a red ball from a bag is mutually exclusive with Event B of not drawing a red ball from the bag. This can be termed as Event A = E and Event B = E'. Then E and E' are complementary to each other. </p>

25 <h3>Mutually Exclusive Events</h3>

26 <p>Mutually exclusive events are those events that will not happen together. They do not have any common outcome.</p>

27 <p>For example, Event A of rolling a die of number 4 is E = {4}, and Event B of rolling a die of number 3 is E = {3}. These are mutually exclusive because both Event A and Event B cannot occur at the same time.</p>

28 <h3>Exhaustive Events</h3>

29 <p>Exhaustive events are those events that cover all possible outcomes of an experiment. This means that during an experiment, at least one of these events must occur.</p>

30 <p>For example, in an examination, the possible outcomes are passing or failing an exam.</p>

31 <h3>Equally Likely Events</h3>

32 <p>Events with equally conceivable outcomes are ones that have an equal likelihood of occurring.</p>

33 <p>For example, tossing a coin has a 50% chance of getting heads and 50% chance of getting tails. </p>