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Transcript of 11 5probabilitywithcountingmethods 091105162308 Phpapp01
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11.5 Probability with the
Fundamental Counting Principles,
Permutations and Combinations
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Three Kinds of Probability
Theoretical Probability
Empirical Probability
Subjective Probability
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Probability with FCP (Problem # 2)
Mr. P has 4 ties(Cartoon character,Navy Blue, Black,Striped), 4 shirts (white,blue, black and gray)and 4 pairs of pants(black, brown, beigeand gray). What is the
probability that he willwear a black tie, blackshirt and black pants?
1/64
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Probability of a Permutation
Number of ways the permutation can occur Total number of permutations
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Probability with Permutations
(Problem # 3)
Jay-Z, Jeremih, R. Kelly
and T.I. were invited to
the 50thcelebration at
Seton. They arrivedrandomly and each
person arrived at
different time.
In how many ways can
they arrive?
In how many ways can
Jay-Z arrive first and T.I.last?
What is the probability
that Jay-Z arrive first
and T.I. last?
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Answer:
a. Total Permutation: 4! = 24
b. No. of permutations forJay Z to arrive first and T.I.
last = 1 x 2 x 1 x 1 = 2
c. Probability = 2/24 = 1/12
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Probability with Permutations
(Problem # 4) Suppose that you want to
arrange the 4 Twilightbooks.
a. What is the probability
that Breaking Dawn (thelast book in the series) isplaced at the end?
b. What is the probabilitythat Twilight (the first
book in the series) isplaced first and Newmoon (the second in theseries) placed second?
A. 6/24 or
B. 2/24 or 1/12
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Probability with Permutations
(Problem # 5)
Miley Cyrus, Taylor
Swift, Demi Lovato,
Lady GaGa and Kelly
Clarkson agree to hold aconcert. What is the
probability that Lady
GaGa will perform first
and Kelly Clarkson last?
6/120 = 1/20
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Probability of a combination
Number of ways the combinations can occur Total number of combinations
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Probability with Combinations
(Problem # 6)
A poker hand consists offive cards.
a. Find the total numberof 5-card poker hands.
b. A heart flush is a 5-card hand that consists ofall hearts. Find thenumber of possible heart
flush. c. Find the probability of
being dealt a heart flush?
A. Total Combination:
2,598,960
B. Possible Combinationfor heart flush: 1287
C. Probability:
1287/2,598,960
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Probability with Combinations
(Problem # 7) To play the Powerball, a
player needs to select fivenumbers from 1-59 and apowerball number from1-39.
a. What is the chance ofwinning the top prize ifyou buy one ticket?
b. What is the chance of
winning the top prize ifthe cost for one ticket is$1 and you spent $100?
A. 1/195,249,054
B. 50/97,624,527
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Probability with Combinations
(Problem # 9)
A group consists of 6 men
and 10 women. Four
members are selected at
random to attend a
conference. Find the
probability that the
selected group consists of
A. All men B. All women
C. 2 men and 2 women
A. 3/364
B. 3/26
C. 135/364
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Probability with Combinations
(Problem # 10)
A box contains 20 IPods,
where 5 of them are
defective. If 5 are
selected at a random,find the probability that
A. All are defective
B. None are defective
A. 1/15504
B. 1001/5168