Chapter 4. Probability and Counting Rules. Sample Spaces and Probability. Probability experiment – a chance process that leads to well-defined results called outcomes (e.g. flipping a coin, drawing a card). Outcome – the result of a single trial of a probability experiment.
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Probability and Counting Rules
P(queen) = 4/52 = 1/13 = .077 = 7.7%
or P(all three children girls) or P(GGG)?
P(GGG) = 1/8 = 0.125 = 12.5%
P(Ec) = 1 – P(E)
P(E) = 1 - P(Ec)
P(E) + P(Ec) = 1
= 1 – 0.69 = 0.31 = 31%
P(A or B) = P(A) + P(B)
P(king) = 4/52 & P(club) = 13/52
But what about the king of clubs?
P(king or club) = P(king) + P(club) – P(king and club)
= 4/52 + 13/52 – 1/52
= 16/52 = 4/13 = 0.308 = 30.8%
P(A or B) = P(A) + P(B) – P(A and B)
P(A and B) = P(A) ∙ P(B)
= 0.097 = 9.7%
P(B|A) = P(A and B) / P(A)
N = parking in a no-parking zone
T = getting a ticket
P(T|N) = P(N and T) / P(N) = 0.06/0.20
= 0.30 = 30%
P(A and B) = P(A) ∙ P(B|A)
n! = n(n-1)(n-2) ∙∙∙ 1
nPr = n!/(n-r)!
nCr = n!/(n-r)!r!