Probability — Class 11 Mathematics
Mathematics · Chapter 14
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Chapter summary
Building on random experiments and sample spaces, this chapter takes the axiomatic approach to probability. Any subset
Events and types of eventsAlgebra of eventsMutually exclusive and exhaustive eventsAxiomatic approach to probabilityProbability of equally likely outcomesAddition and complement rules
Key ideas & terms
- Event
- Any subset
of the sample space . - Impossible and sure events
is impossible; is the sure event. - Mutually exclusive events
- Events with
that cannot occur together. - Exhaustive events
- Events whose union is the whole sample space
. - Equally likely outcomes
- Outcomes with the same probability, so
. - Addition rule
.
Extra questions & answers
What is an event in probability?
Any subset
Define the impossible and sure events.
The empty set
When are two events mutually exclusive?
When they cannot occur simultaneously, i.e.
State the axioms of probability.
For every event
Give the probability for equally likely outcomes.
State the addition rule for any two events.
State the complement rule.
One card is drawn from 52. Find the probability it is a diamond.
There are 13 diamonds, so
A coin is tossed twice. Find the probability of at least one tail.
Sample space
When are events exhaustive and mutually exclusive together?
When
Write the formula for the theoretical probability of an event E.
What is the probability of a sure event and of an impossible event?
What is the range of the probability of any event?
The probability of any event lies between 0 and 1, that is
What are complementary events, and how are their probabilities related?
An event
A die is thrown once. What is the probability of getting an even number?
Favourable outcomes are 2, 4, 6 (three of them) out of six, so
A card is drawn from a well-shuffled pack of 52. What is the probability that it is a king?
There are 4 kings, so
Two coins are tossed together. What is the probability of getting two heads?
The outcomes are HH, HT, TH, TT; only one is favourable, so