Chapter 4 – Probability and Counting Rules section 4.3 – Multiplication Rules and Conditional Probability. Multiplication Rules for Probability. Independent Events Two events are independent if the fact that A occurs does not affect the probability of B occuring. Flip a coin 5 times…
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Two events are independent if the fact that A occurs does not affect the probability of B occuring.
Multiplication Rule 1
When two events are independent, the probability of both occuring is
P(A and B) = P(A)P(B)
Multiplication Rule 2
when two events are dependent, the probability of both occurring is
P(A and B) = P(A)·P(B|A)
The probability that the second event B occurs given that the first event A has occurred is found by:
P(B|A) = P(A and B)
The probability that Sam parks in a no-parking zone and gets a ticket is 0.06 and the probability that Sam cannot find a parking space and has to park in the no-parking zone is 0.20. On Tuesday, Sam arrives at school and has to park in a no-parking zone. Find the probability that he will get a ticket.
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