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Probability

Probability is a measure from 0 to 1 of how likely an event is to occur. It can be calculated by taking the number of desired outcomes divided by the total number of possible outcomes. There are concepts like complementary events, independent events, conditional probability, and the multiplication rule to calculate probabilities when events are combined or dependent. Examples of probability calculations are provided for drawing cards from a deck or blocks from a bag with different colors.

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47 views1 page

Probability

Probability is a measure from 0 to 1 of how likely an event is to occur. It can be calculated by taking the number of desired outcomes divided by the total number of possible outcomes. There are concepts like complementary events, independent events, conditional probability, and the multiplication rule to calculate probabilities when events are combined or dependent. Examples of probability calculations are provided for drawing cards from a deck or blocks from a bag with different colors.

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BJYXSZD
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© © All Rights Reserved
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Probability

Probability – a measure of how likely a particular event  Inclusive events


will occur. We denote the probability of an event E Two events, A and B, are events from a sample
occurring as P(E). It can take on any value between 0 space S. The probability that either A or B will occur,
and 1 inclusive. denoted by is:

Experiment – involves performing a number of trials to


enable us to measure the chance of an event occurring  Independent Events
in the future. If the occurrence or nonoccurrence of event A
does not affect the occurrence or nonoccurrence of
Sample Space – the set S whose elements are all event B, then A and B are independent events.
possible outcomes of an experiment.

Event – set of outcomes that are a subset of the sample


space.  Conditional Probability
Let A and B be two events in S, such that P(A) is
non-zero. If event A is a condition for event B, then

where: P(E) – probability of an event to happen


S – sample space
E – event  Multiplication Rule
n(S) – cardinality of the sample space If in an experiment the events A and B can both
n(E) – cardinality of the event occur then,

Events
 Complementary Events
Given the event E in a sample space S, the
complement of E, denoted by EC, consists of all Exercises:
1. A card is drawn from a well-shuffled deck of 52
outcomes in S but not in E. cards. What is the probability of drawing a card
with a number printed on it that is less than
four?
2. A block is chosen at random from a bag
containing 6 white blocks, 4 purple blocks and
If the probability that an event occurs is p (where p
12 red blocks. What is the probability that it
≠ 0 and p ≠ 1), then will be a red or a white block?
3. A tire manufacturer found that 10% of the tires
Odds in favor of the event = p : (1 – p) produced had cosmetic defects and 2% had
Odds against the event = (1 – p) : p both cosmetic and structural defect. What is
the probability that one tire selected at random
is structurally defective if it is known that it has
 Mutually Exclusive Events a cosmetic defect?
Two events, A and B are mutually exclusive if 4. Imagine two women, each of whom tells the
and only if they have no outcomes in common. truth only two-thirds of the time. If both say
that it is raining, what is the probability that it
Therefore, they cannot occur at the same time. is really raining?

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