Pakistan MCQs

Expected value combines each outcome with its probability.
Over many repetitions, the average tends toward this value.

A fair coin has two equally likely outcomes.
One of the two outcomes is heads, so the probability is 1/2.

A random experiment can be repeated under similar conditions.
The exact outcome is uncertain before observation.

The sample space lists every outcome that can occur.
Events are subsets of this space.

An event consists of one or more possible outcomes.
Its probability measures how likely it is to occur.

The complement contains all sample-space outcomes outside A.
Its probability is 1 - P(A).

Mutually exclusive events have an empty intersection.
Thus P(A ∩ B) = 0.

Independent events satisfy P(A|B) = P(A).
Their intersection probability equals the product of their probabilities.

Conditional probability updates the relevant sample space using known information.
It is written as P(A|B).

The addition rule combines probabilities of events in a union.
Any overlap must be subtracted once.

Independence allows multiplication of the separate event probabilities.
This gives the probability that both occur.

Bayes theorem reverses conditional probabilities using prior information.
It combines prior probability with likelihood of evidence.