Compound Event

Probability denotes how likely an event will happen. In probability, 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.

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

• $E$: Exactly one head appeared
• $F$: At least one head appeared
• $G$: Utmost one head appeared etc.

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

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 $P$(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 $={\frac {3}{6}}X{\frac {1}{2}}={\frac {3}{12}}$