Transcript Probability Concepts & Applications

Independent Events
That the occurrence of one event has no
effect on the probability of occurrence of
the second event.
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Probabilities: Independent Events
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Marginal probability – the probability of an event
occurring: P(A)
Joint probability – the probability of multiple,
independent events, occurring at the same time:
P(AB) = P(A)*P(B)
Conditional probability –
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The probability of event B given that event A has
occurred: P(B/A) = P(B)
Or, the probability of event A given that event B has
occurred: P(A/B) = P(A)
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Problem 2-16
An urn contains 8 red chips, 10 green
chips, and 2 white chips. A chip is drawn
and replaced, and then a second chip
drawn. What is the probability of ……
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P(R) 8/20 = .40
P(G) 10/20 = .50
P(W) 2/20 = .10
1.00
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a)
A white chip on the first draw?
Marginal probability - P(A)
P(W) = .10
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b) A white chip on the first draw and a red
on the second?
Joint probability for two independent events
– P(AB) = P(A)*P(B)
P(WR) = P(W) * P(R)
.10 * .40 = .04
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c)
two green chips being drawn?
Joint probability for two independent events –
P(AB) = P(A)*P(B)
P(GG) = P(G) * P (G)
.50 * .50 = .25
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d) A red chip on the second, given that a
white chip was drawn on the first?
Conditional probability – for independent
events
P(AB) = P(B)
P(R/W) = P(R)
P(R/W) = .40
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