About Probability of an Event
What is an Event in Probability?
An event in probability is a collection of one or more outcomes of an experiment. In other words, a set of outcomes is called an event. The outcomes of a specific event are called favorable outcomes.
Let us understand this with an example.
Annie throws a dice while playing ludo. In this scenario throwing the dice is an experiment and the possible numbers that can appear on the top of the dice are 1, 2, 3, 4, 5 and 6. Hence, the outcomes of this experiment are 1,2,3,4,5 and 6.
The appearance of a number on the top of the dice is called an event.
If Annie needs 4 to win the match, the appearance of 4 on the top of the dice is an event for her. And 4 is the required outcome of the event. So, 4 is called a favorable outcome.
Total number of outcomes = 6
Number of favorable outcomes = 1
Types of Events in Probability
There are two types of events in probability:
- Single event
- Compound event
1. Single event: When we consider only one event at a time in an experiment, it is called a single event. For example, getting 6 on the top of a dice to win a game is a single event.
2. Compound events: Unlike a single event, a compound event consists of two or more events. For example, on rolling a dice and tossing a coin, getting 6 on dice and tails together is a compound event.
Probability of an Event
Probability of an event is defined as the quotient of the number of favorable outcomes and total number of outcomes. Probability is denoted as ‘P’.
P(event) = \(\frac{\text{Number of favorable outcomes}}{\text{total number of outcomes}}\)
Note: Probability formula for a single event and a compound event is the same.
Solved Examples
Example 1: Robert tossed a coin and a dice together. Find the probability of the coin landing on heads and getting a 4 on the dice.
Solution:
Make a table of sample space and represent H as heads and T as tails.
Heads and 4 are shown as 4H.
From the table it is evident that the total number of possible outcomes is 12.
Number of favorable outcomes is 1.
Therefore,
P(event) = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\)
P(4H) = \(\frac{1}{12}\)
Example 2: Amelia and Hazel were playing with the spinner. Hazel wins if the pointer stops at an even number. What is the probability of Hazel winning the game?
Solution:
Hazel wins if the pointer stops at an even number, that is, 2, 4 and 6.
Number of favorable outcomes = 3
Total possible outcomes are 1, 2, 3, 4, 5 and 6
Total number of possible outcomes = 6
P(event) = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\)
P(Hazel wins ) = \(\frac{3}{6}=\frac{1}{2}\)
So, the probability for Hazel to win the game is \(\frac{1}{2}\).
Example 3: One card is drawn from a deck of a well shuffled deck of the usual 52 cards. Find the probability that the card that is drawn is a queen.
Solution:
There are four cards in each suit with a queen in a pack of 52 cards.
So, the number of favorable outcomes = 4
Total number of possible outcomes = 52
P(event) = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\)
P(card is queen) = \(\frac{4}{52}=\frac{1}{13}\)
So, the probability of a card being a queen, is \(\frac{1}{13}\).
Probability events are a collection of one or more outcomes of an experiment.
The value of a probability can be minimum to zero and maximum to one, that is, the probability of an event lies between 0 and 1.
Outcomes are the total possible results of an experiment, while an event is a collection of one or more outcomes of an experiment.
The probability of an event can be expressed in terms of fractions, decimals and percentages.
No, the minimum number value of a probability is 0. Hence, the probability of an event cannot be a negative number.