# probability and combination based questions

I have completed some of the question. I need help with the formulas on how to solve the problems along with making sure what I have done is correct.

5.2 Textbook p 282 Exercises 22, 24, 32

A golf ball is selected at random from a golf bag. If the golf bag contains 9 Titleist's, 8 Maxflis, and 3 Top Flites, find the probability of each event.

22. The golf ball is a Maxfli or Top-Flite

P(E or F) = P(E) + P(F) = P (Maxfli or Top Flite) =P(Maxfli) + P(Top Flite)

n(S)= 9+8+3=20

Probability of finding Maxfli = n(Maxfli)/n(s)= 8/20=2/5

Probability of finding Top Flites= P(Top Flites)= n(Top Flites)/n(s)= 3/20

24. The golf ball is not a Top Flite.

Probability of Top Flite= P(A) n(A)/n/(S) = 3/20

P (E^c)= 1-P(E)

A= 1- 3/20 =17/20

32.

B) 5.3 Selected problems PDF exercises 7 and 19, click here

7.) A bag contains 4 red balls and 6 white balls. Two balls are drawn without replacement.

The number of white balls in the bag = 6. Total number of balls in the bag = 10.

The probability that the first ball is white is 6/10=3/5

After first selection of the balls there are 5 white balls left and 9 balls left this = 5/9

The probability that first ball drawn is white and the second ball drawn is white without replacement is: P(E and F)= P(E) x P(F/E)= 3/5 x 5/9= 1/3

a) What is the probability that the second ball is white, given that the first ball is red?

b) What is the probability that the second ball is red, given that the first ball is white?

c) Answer (a) if the first ball is replace before the second is drawn.

8.) A fair die is rolled. Find the probability that the result is a 4, given that the result is even.

P(4) = 1/6

9.) A fair coin is tossed 3 times. Find the probability of

a) Throwing 3 heads, given that the first toss is head.

P(heads) = ½ P(tails)= ½

b) Throwing 3 heads, given that the first two tosses result in heads.

10.) A fair coin is tossed 14 times. What is the probability of tossing 14 heads, given that the first 13 tosses are heads?

11.) A die is thrown, twice. What is the probability that a 3 will result the first time and a 6 the second time? P(3 the first time)= 1/6 P(6 the second time) = 16 P( 3 the first time and 6 the second time) = 1/6*1/6 = 1/36

12.) A die is rolled and a coin is tossed. What is the probability that the die shows an even number and the coin toss results in a head?

- The sample space S of the experiment described in question 5 is as follows

S = { (1,H),(2,H),(3,H),(4,H),(5,H),(6,H)

(1,T),(2,T),(3,T),(4,T),(5,T),(6,T)}

- Let E be the event "the die shows an odd number and the coin shows a head". Event E may be described as follows

E={(1,H),(3,H),(5,H)}

- The probability P(E) is given by

P(E) = n(E) / n(S) = 3 / 12 = 1 / 4

19.) A bag contains 9 nickels, 4 dimes, and 5 quarters. If you draw 3 coins at random from the bag, without replacement, what is the probability that you will get a nickel, a quarter, and a nickel, in order?

Instructions: Multiply the two probabilities, type at least two steps in the same Word document

C) 5.5 Textbook pg 313 Exercises 28, 30, 48

28.) List all the permutations of four objects a, b, c, and d, taken two at a time without repetition. What is 4P2?

30.) List all the combinations of four objects a, b, c, and d taken two at a time. What is 4C2?

48.) Forming a committee: Four members from a 20-person committee are to be selected randomly to serve as chairperson, vice chairperson, secretary, and treasurer. The first person selected is the chairperson: The second, vice chairperson, third secretary and fourth the treasure. How many different leadership structures are possible?

nPr=n!/(n-r)! = n=20 r= 4 20P4

20P4= 20!/(20-4)!= 20!/16!= 20 x 19 x 18 x 17 x 16/16=

20 x 19 x 18 x 17 =116,280

© BrainMass Inc. brainmass.com October 25, 2018, 6:45 am ad1c9bdddfhttps://brainmass.com/math/probability/probability-and-combination-based-questions-474119

#### Solution Preview

Hi there,

Week 7 Assignment

5.2 Textbook p 282 Exercises 22, 24, 32

A golf ball is selected at random from a golf bag. If the golf bag contains 9 Titleist's, 8 Maxflis, and 3 Top Flites, find the probability of each event.

22. The golf ball is a Maxfli or Top-Flite

P(E or F) = P(E) + P(F) = P (Maxfli or Top Flite) =P(Maxfli) + P(Top Flite)

n(S)= 9+8+3=20

Probability of finding Maxfli = n(Maxfli)/n(s)= 8/20=2/5

Probability of finding Top Flites= P(Top Flites)= n(Top Flites)/n(s)= 3/20

Probability of either a Maxfli or Top-Flite=(8/20+3/20)=11/20

24. The golf ball is not a Top Flite.

Probability of Top Flite= P(A) n(A)/n/(S) = 3/20

P (E^c)= 1-P(E)

A= 1- 3/20 =17/20

32.

B) 5.3 Selected problems PDF exercises 7 and 19, click here

7.) A bag contains 4 red balls and 6 white balls. Two balls are drawn without replacement.

The number of white balls in the bag = 6. Total number of balls in the bag = 10.

The probability that the first ball is white is 6/10=3/5

After first selection of the balls there are 5 white balls left and 9 balls left this = 5/9

The probability that first ball drawn ...

#### Solution Summary

The solution provides detailed explanation how to solve probability and combination based questions.

Factorials, combinations and permutations.

Calculating factorials, combinations, permutations.

Evaluate the given expressions and express all results using the usual format for writing

numbers (instead of scientific notation).

Factorial Find the number of different ways that the nine players on a baseball team can

line up for the National Anthem by evaluating 9!.

Card Playing Find the number of different possible five-card poker hands by evaluating

52 C 5.

Scheduling Routes A political strategist must visit state capitols, but she has time to

visit only 3 of them. Find the number of different possible routes by evaluating 50 P3.

Trifecta Refer to Exercise 3. Find the number of different possible trifecta bets in a race

with ten horses by evaluating 10 P3.

In Exercise 22, use the data in the accompanying table, which summarizes

challenges by tennis players (based on data reported in USA Today). The

results are from the first U.S. Open that used the Hawk-Eye electronic system

for displaying an instant replay used to determine whether the ball is in

bounds or out of bounds. In each case, assume that one of the challenges is

randomly selected.

Was the challenge to

The call successful?

Yes no

Men 201 288

Women 126 224

Tennis Instant Replay If M denotes the event of selecting a challenge made by a man,

find p (M).

In Exercise 28, refer to the following table summarizing results from a study

of people who refused to answer survey questions (based on data from "I Hear

You Knocking but You Can't Come In," by Fitzgerald and Fuller, Sociological

Methods and Research, Vol. 11, No. 1). In each case, assume that one of the subjects

is randomly selected.

AGE

18-21 22-29 30-39 40-49 50-59 60+

Responded 73 255 245 136 138 202

Refused 11 20 33 16 27 49

Survey Refusals A pharmaceutical company is interested in opinions of the elderly, because

they are either receiving Medicare or will receive it soon. What is the probability that

the selected subject is someone 60 and over who responded?

express the indicated degree of likelihood as a probability

value between 0 and 1.

Weather A WeatherBug forecast for the author's home was stated as: "Chance of rain: 80%."

Births When a baby is born, there is approximately a 50-50 chance that the baby is a girl.

Roulette When playing roulette in the Mirage Casino, you have 18 chances out of 38 of

winning if you bet that the outcome is an odd number.

Identifying Probability Values

a. What is the probability of an event that is certain to occur?

b. What is the probability of an impossible event?

c. A sample space consists of 10 separate events that are equally likely. What is the probability

Of each?

d. On a true/false test, what is the probability of answering a question correctly if you make a random guess?

e. On multiply-choice test with five possible answers for each, what is the probability of answering a question correctly If you make random guess?

Genotypes In Example 4 we noted that a study involved equally likely genotypes represented

as AA, Aa, aA, and aa. If one of these genotypes is randomly selected as in Example 4,

what is the probability that the outcome is AA? Is obtaining AA unusual?

Example 4: Genotypes When studying the affect of heredity on height,

we can express each individual genotype, AA, Aa, aA, and aa, on an index card and

shuffle the four cards and randomly select one of them. What is the probability

that we select a genotype in which the two components are different?