(a) Explain why -0.41 cannot be the probability of some...

(a) Explain why -0.41 cannot be the probability of some event.
(b) Explain why 1.21 cannot be the probability of some event.
(c) Explain why $120 \%$ cannot be the probability of some event.
(d) Can the number 0.56 be the probability of an event? Explain.

Key Concepts

Probability Range

In probability theory, a probability is defined as a number between 0 and 1 inclusive. This range reflects the fact that an event cannot be less than impossible (0) or more than certain (1). Any value outside this interval does not align with the basic axioms of probability, making such values invalid for representing the chance of an event occurring.

Negative Probabilities

The concept of probability excludes negative numbers because a negative probability would imply the occurrence of an event is less than impossible, which is conceptually meaningless. Probabilities must be non-negative, ensuring that they accurately measure the likelihood of real-world events.

Probabilities Greater Than One

Any number greater than 1 cannot represent a probability because it would suggest that the event has a likelihood exceeding certainty. The upper bound of the probability scale is 1, representing events that are guaranteed to occur, and any value above this contradicts the definition of probability.

Conversion Between Percentages and Decimals

Probabilities can be expressed in different forms, such as decimals or percentages. When expressed as a percentage, the value is typically between 0% and 100%, which corresponds to 0 and 1 in decimal form. A percentage like 120% converts to 1.20 in decimal form, exceeding the maximum of 1 and thus is not a valid probability.

Transcript

00:01 Let us look at part a.

00:04 What is probability? probability is number of favorable, is number of favorable outcomes, number of favorable outcomes, which means that this is a count of something upon total number of outcomes.

00:22 Upon total number of outcomes, right? both of them are counts.

00:30 And if they are counts, can they ever be negative? can i eat my mind? 7 chocolates no i cannot right that is why this number or this fraction will never be negative and hence 0 .41 minus 0 .41 can never be a probability or my probability can never be negative and hence the first answer is no right this cannot be a probability now can 1 .21 be a probability let us move on to part be can 1 .21 be a probability well let's think of it number of favorable outcomes and total number of outcomes let's say i'm playing 10 matches and i want to find the probability or okay i'm playing 10 matches 10 matches and i am winning five of them so what is the probability that i will win i am winning 50 % of the times so my probability is 1 by 2 now is it possible that i play 10 matches and i win 12.

01:40 No.

01:41 So can my favorable outcomes ever be greater than the total number of outcomes? no, which means that this fraction over here can never be more than one.

01:49 So how can my probability be 1 .21? not possible.

01:54 Moving on to part c.

01:57 Moving on to part c.

01:59 Can 120 % be a probability? no.

02:04 Probability is always between 0 and 100%...

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