11 5probabilitywithcountingmethods 091105162308 phpapp01

8/11/2019 11 5probabilitywithcountingmethods 091105162308 Phpapp01

1/15

11.5 Probability with the

Fundamental Counting Principles,

Permutations and Combinations


2/15

Three Kinds of Probability

Theoretical Probability

Empirical Probability

Subjective Probability


3/15


4/15

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


5/15

Probability of a Permutation

Number of ways the permutation can occur Total number of permutations


6/15

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?


7/15

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


8/15


(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


9/15


(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


10/15

Probability of a combination

Number of ways the combinations can occur Total number of combinations


11/15

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


12/15


(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


13/15


14/15


(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


15/15


(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

11 5probabilitywithcountingmethods 091105162308 phpapp01

Documents