Question

When randomly selecting an​ adult, a denotes the event of selecting someone with blue eyes. What do and ​represent?.

Answer 1

P(A) represents the probability of selecting an adult with blue eyes.

P(Ā) represents the probability of selecting an adult who does not have blue eyes.

What is probability?

Probability is a measure of how likely an event is to occur. Many events are impossible to predict with absolute certainty. We can only predict the chance of an event occurring, i.e., how likely it is to occur, using it. Probability can range from 0 to 1, with 0 indicating an impossible event and 1 indicating a certain event.  The probability of all events in a sample space equals one.

$Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes$

There are three major types of probabilities:

• Theoretical Probability
• Experimental Probability
• Axiomatic Probability

What is Theoretical Probability?

It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.

What are Complementary Events?

The possibility that there will be only two outcomes, stating whether or not an event will occur. Examples of complementary events include a person coming or not coming to your house, getting a job or not getting a job, and so on. Essentially, the complement of an event occurring in the exact opposite probability that it will not occur. Here are some more examples:

• Today will either rain or not rain.
• The student will either pass or fail the exam.
• You either win or you don't.

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Answer 2

The correct answer is P(A) represents the probability that the adult selected has blue eyes.

P(Aˉ) represents the probability that the adult selected does not have blue eyes.

What is Probability?

The ratio of favorable outcomes to all possible outcomes of an event is known as the probability.

P(A) denotes the probability of an event A; in this case, it is given that A is the event of selecting someone with blue eyes.

P(Aˉ) denotes the probability that A does not occur. It signifies that the adult chosen in this instance won't have blue eyes.

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The correct question is:-

When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do P(A) and P(Aˉ) represent?