Difference between revisions of "Compound Event"

Latest revision as of 22:15, 16 April 2024

Probability denotes how likely an event will happen. In probability, simple, compound and complementary events are different types of probabilities.

If an event has more than one sample point, it is called a Compound event.

For example, in the experiment of “tossing a coin thrice” the events

are all compound events.

The subsets of $S$ associated with these events are

$E=\{HTT,THT,TTH\}$ , $f=\{HTT,THT,TTH,HHT,HTH,THH,HHH\}$

$G=\{TTT,THT,HTT,TTH\}$

Each of the above subsets contain more than one sample point, hence they are all compound events.

Probability of an event = The number of favorable outcomes / The number of total outcomes

Find the probability of rolling an even number on a die, then tossing a head on a coin.

Probability of an event = The number of favorable outcomes / The number of total outcomes

Here $P$ (even number) $={\frac {3}{6}}$

favorable outcomes for getting even number on a die = $2,4,6$ hence the number of favorable outcomes = $3$

$P$ (head) $={\frac {1}{2}}$

Hence required probability $={\frac {3}{6}}X{\frac {1}{2}}={\frac {3}{12}}$

@@ Line 1: / Line 1: @@
+Probability denotes how likely an event will happen. In probability, [[Simple Event|simple,]] compound and complementary events are different types of probabilities.
 == Definition ==
 If an event has more than one sample point, it is called a Compound event.
@@ Line 4: / Line 6: @@
 For example, in the experiment of “tossing a coin thrice” the events
-* <math>E</math> : Exactly one head appeared
+* <math>E</math>: Exactly one head appeared
 * <math>F</math>: At least one head appeared
 * <math>G</math>: Utmost one head appeared etc.
@@ Line 16: / Line 18: @@
 <math>G=\{TTT,THT,HTT,TTH\}</math>
-Each of the above subsets contain more than one sample point, hence they are all compound events
+Each of the above subsets contain more than one sample point, hence they are all compound events.
+Probability of an event = The number of favorable outcomes / The number of total outcomes
+== Example ==
+Find the probability of rolling an even number on a die, then tossing a head on a coin.
+Probability of an event = The number of favorable outcomes / The number of total outcomes
+Here <math>P</math>(even number)<math>=\frac{3}{6}
+</math>
+favorable outcomes for getting even number on a die = <math>2,4,6</math> hence the number of favorable outcomes = <math>3</math>
+<math>P</math>(head) <math>=\frac{1}{2}
+</math>
+Hence required probability <math>=\frac{3}{6} X \frac{1}{2}=\frac{3}{12}
+</math>