0-6 Multiplying Probabilities, Lecture notes of Probability and Statistics

0-6 Multiplying Probabilities. Objective: Find probabilities of independent and dependent events. Use two-way frequency tables to find.

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2021/2022

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0-6 Multiplying Probabilities
Objective: Find probabilities of independent and
dependent events. Use two-way frequency tables to find
conditional probabilities.
If the occurrence of one event does not affect the
probability of a second event occurring, then the two
events are independent events.
Example 1:
A coin is tossed and a die is rolled. What is the probability
of the coin landing on tails and rolling a 3?
If the occurrence of the first event does affect the
probability of the second event occurring, then the events
are dependent events.
*An example of dependent events is drawing a card from a
standard deck of cards, not putting it back, and then
drawing a second card.
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0 - 6 Multiplying Probabilities

Objective : Find probabilities of independent and dependent events. Use two-way frequency tables to find conditional probabilities. If the occurrence of one event does not affect the probability of a second event occurring, then the two events are independent events. Example 1 : A coin is tossed and a die is rolled. What is the probability of the coin landing on tails and rolling a 3? If the occurrence of the first event does affect the probability of the second event occurring, then the events are dependent events. *An example of dependent events is drawing a card from a standard deck of cards, not putting it back, and then drawing a second card.

The probability of event B occurring given that event A has already occurred is called a conditional probability and is represented by P(B|A), read the probability of B given A. This notation is used in the rule for the probability of two dependent events. Example 2 : A bag contains 12 red, 9 blue, 11 yellow, and 8 green marbles. If two marbles are drawn at random and not replaced, what is the probability that a red and then a blue marble are drawn? Example 3 : At a restaurant, 25% of customers order chili. If 4% of customers order chili and a baked potato, find the probability that someone who orders chili also orders a baked potato.