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What does it mean if the probabilities of an event is 1 or 0?

  • Last Updated : 29 Oct, 2021

Probability is a term used to determine the chance of occurring a particular event. It can also be understood as the possibility of the occurrence of an event. The probability is expressed on a linear scale from 0 to 1 as well as in percentage from 0% to 100%. 

Types of Probability

The types of probability are mentioned below. Basically, there are majorly three types, theoretical probability, experimental probability, and subjective probability.

  • Theoretical probability: Theoretical probability or also known as the classical probability is the number of outcomes in sample spaces that are known and each outcome is equally likely to occur.
  • Experimental probability: Experimental probability is also known as statistical or relative frequency. It is the probability in which outcomes are measured by experimenting.
  • Subjective probability: It is the probability that is estimated by making an educated guess by using intuition.

The formula for determining the probability of an  event is given below,

P(A) = n(A)/n(S)

Where,

P(A)  is the probability of an event

n(A) is the number of favorable outcomes

n(S) is the total number of favorable outcomes

Basic Formulae of Probability

The probability formula gives the possibility of an event to occur. It can simply be calculated by some basic estimated formulas. The formulas are enlisted below. P(A) is the probability for event A, P(B) is the probability for event B.

  • Rule of Addition

P(A∪B) = P(A) + P(B) – P(A∩B)

  • Probability Range

0 ≥P(A) ≤1

  • Rule of Complementary Events

P(A’) + P(A) = 1

  • Disjoint Events

P(A∩B) =0

  • Independent Events

P(AB) =P(A) . P(B)

  • Conditional Probability

P(A|B) = P(B|A). P(A)|P(B)

What does it mean if the probabilities of an event is 1 or 0?

Answer:

Let’s look at each case separately and understand what it means for a probability to be 1 and for a probability to be 0,

What does it mean the probability of an event is 1?

The probability of an event is the number expressing the chances of occurring the event. The number is determined between 0 to 1. The probability of an event is 1. It means the chances of the event happening is 100%. The event cannot be escaped and it will definitely take place.

What does it mean the probability of an event is 0?

The probability of an event is 0, which means the chances of the event happening is 0%. The event will not take place in any condition or it is impossible.

Sample Problems

Question 1: What are some real-life examples of probability?

Answer:

Cards games, lottery, Insurance are some real-life examples of probability.

Question 2: What does probability 0.5 means?

Answer:

The probability of an event is 0.5, which means the chances of happening something is 50%. 

Question 3: The probability of an event is 0.75. What does it mean?

Answer:

The probability of an event is 0.75  means the chances of the event occurring is 75.25%.

Question 4: Determine the probability to get an ace from a card taken from a deck.

Answer:

Given,

Total no. of favorable outcomes n(S) = 52

Number of Aces in the deck = 4

Number of favorable outcomes n(A) = 4

Now,

P(Ace)=\frac{n(A)}{n(s)}

=4/52

= 1/13

Hence, the probability is 1/13.

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