Statistics 3.1-3.4 Assignment Questions
What is the probability that a registered voter voted in the election? Square: 3,597,631. Circle: 3,069,421.
Add numbers in the square and the circle. (Total number of registered voters.) So 3,597,631+3,069,421=6,667,052. Now divide 3,069,421/6,667,052=0.460.
Suppose 90% percent of kids who visit a doctor have a fever, and 45% of kids with a fever have sore throats. What's the probability that a kid who goes to the doctor has a fever and a sore throat?
Make the percents into a probability. (90%=.09,45%=0.45). Multiply the percents together. 0.9x0.45=0.405
You randomly select one card from a standard deck. Event A is selecting a seven. Determine the number of outcomes in event A. Then decide whether the event is a simple event or not.
The number of outcomes in event A is 4 because there are four sevens, one of each suit, in a standard deck. This event is not a simple event because it has more than one outcome.
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing an odd number between 20 and 30.
The sample space is {21,23,25,27,29} (All the odd numbers between 20 and 30). There are 5 outcomes in the sample space.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. If two events are mutually exclusive, they have no outcomes in common.
True
Researches found that people with depression are seven times more likely to have a breathing-related sleep disorder than people who are not depressed. Identify the two events described in the study. Do the results indicate that the events are independent or dependent? (a) Identify the two events. Choose the correct answer below. (b) Are the events independent or dependent?
(a) Depression and breathing-related sleep disorder. (b) Dependent
Determine whether the events E and F are independent or dependent. Justify your answer. (a) E: A person living at least 70 years. F: The same person regularly handling venomous snakes. (b)E: A randomly selected person finding cheese revolting. F: A different randomly selected person finding cheese delicious c)E: The consumer demand for synthetic diamonds. F: The amount of research funding for diamond synthesis.
(a) E and F are dependent because regularly handling venomous snakes can affect the probability of a person living at least 70 years. (b) E cannot affect F and vice versa because the people were randomly selected, so the events are independent. (c) The consumer demand for synthetic diamonds could affect the amount of research funding for diamond synthesis, so E and F are dependent.
During a 52-week period, a company paid overtime wages for 19 weeks and hired temporary help for 8 weeks. During 6 weeks, the company paid overtime and hired temporary help. Complete parts (a) and (b) below. (a) Are the events "selecting a week that contained overtime wages" and "selecting a week that contained temporary help wages" mutually exclusive? (b) If an auditor randomly examined the payroll records for only one week, what is the probability that the payroll for that week contained overtime wages or temporary help wages?
(a) No (b) Find the probability of overtime wages. 19/52. Find the probability of temporary help. 8/52. Find the probability of overtime wages and temporary help. 6/52. 19/52+8/52-6/52=0.404.
The percent distribution of live multiple-delivery births (three or more babies) in a particular year for women 15 to 54 years old is shown in the pie chart. Find each probability. (a) Randomly selecting a mother 30-39 years old (b) Randomly selecting a mother not 30-39 years old (c) Randomly selecting a mother less than 45 years old (d) Randomly selecting a mother at least 20 years old
(a) Since 30-34 is 37.2%, change to decimal. =.372. Since 35-39 is 24.4%, change to decimal. =.244. Then add two events. .372+.244=0.616 (b) Take the amount from "Randomly selecting a mother 30-39 years old" and minus it from 1. 1-0.616=0.384. (c) Take the amount of 45 and above, which is 4.0%, change it to a decimal. =0.040. Then minus this from 1. 1-0.040=0.96. (d) Take the amount of 20 and below, which is 1.4% and change to a decimal. =0.014. Then minus this from 1. 1-0.014=0.986
In the general population, one woman in eight will develop breast cancer. Research has shown that 1 woman in 550 carries a mutation of the BRCA gene. Nine out of 10 women with this mutation develop breast cancer. (a) Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene. (b) Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer. (c) Are the events of carrying this mutation and developing breast cancer independent or dependent?
(a) Since 9 out of 10 women with this mutation develop breast cancer, divide 9/10. 9/10= 0.9 (b) Since 1 in 550 woman carry this mutation, divide 1/550 and times by 0.9. 1/500 x 0.9= 0.0009. (c) Dependent
Use the bar graph below, which shows the highest level of education received by employees of a company, to find the probability that the highest level of education for an employee chosen at random is F. A=8, B=21, C=35, D=18, E=7, F=2.
Add all of the frequencies together. 8+21+35+18+7+2=91. Divide by the frequency of F. (which is 2) 2/91=0.022.
Determine the number of outcomes in the event. Decide whether the event is a simple event or not. A computer is used to select randomly a number between 1 and 9, inclusive. Event A is selecting a 7.
An event that consist of a single outcome is called a simple event. The number of outcomes in event A is exactly one. Therefore, A is a simple event.
The probability that a person in the United States has type B+ blood is 14%. Five unrelated people in the United States are selected at random. Complete parts (a) through (d). (a) Find the probability that all five have type B+ blood. (b) Find the probability that none of the five have type B+ blood.(c) Find the probability that at least one of the five has type B+ blood. (d) Which events can be considered unusual? Explain.
Convert percent into a probability, remove the % sign and then divide by 100. 14%=0.14. (a) Since we are finding the probability that all five people have type B+ blood, the number of independent events is 5. Take the percent that a person in the US has type by blood and multiply it 5 times. 0.14x0.14x0.14x0.14x0.14=0.000054 (b) Because the probability that a person has type B+ blood is 0.14, the probability that a person does not have type B+ blood is 1-1-1-0.14=0.86. Times 0.86 five times. 0.86x0.86x0.86x0.86x0.86=0.470. (c) Take the probability that a person does not have type B+ blood (0.470) and minus it from 1. 1-0.470=0.530. (d) An event is considered unusual if its probability is less than or equal to 0.05. Review your answers for parts (a), (b), and (c) to determine whether any of the events can be considered unusual. In this problem, the event in part (a) is unusual because 0.000054 is less than 0.05.
Use the frequency distribution, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the 18 to 20 years old age range. 18-20=6.3 21-24=9.5 25-34=21.4 35-44=24.5 45-64=54.6 65+=28.1
First determine the number of trials of this experiment. (Add all of the frequencies together). This equals 144.4 million. Now, determine which frequency should be in the numerator of the probability equation. The frequency of the event is "18 to 20" is 6.3. Take 6.3/144.4=0.044. Therefore, the probability that a voter chosen at random is in the 18 to 20 years old range is 0.044.
Decide if the events shown in the Venn diagram are mutually exclusive.
No
Decide if the events are mutually exclusive. Event A: Randomly selecting someone who owns a car Event B: Randomly selecting a married male
No, because someone who owns a care can be a married male.
By rewriting the formula for the multiplication rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B|A)=P(A and B)/P(A). Use the information below to find the probability that a flight departed on time given that it arrives on time. The probability that an airplane flight departs on time is 0.90. The probability that a flight arrives on time is 0.85. The probability that a flight departs and arrives on time is 0.79.
P(A and B)=0.79 P(A)=0.85 0.79/0.85=0.929.
Find P(A or B or C) for the given probabilities. P(A)=0.39, P(B)=0.28,P(C)=0.17 P(A and B)=0.13, P(A and C)=0.03, P(B and C)=0.05 P(A and B and C)=0.01
P(A or B or C)= 0.39+0.28+0.17-0.13-0.03-0.05+0.01=0.64
You toss a coin and randomly select a number from 0 to 4. What is the probability of getting tails and selecting a 3?
P(E)= Number of outcomes in event E/Total number of outcomes in sample space. There are two choices for the coin and five choices for the number. Total possible outcomes in the sample space is 2x5=10 Find the number of ways of getting tails and selecting a 3. The number of outcomes in this event is 1x1=1 P=1/10=0.1 The probability of the described event is 0.1.
Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. The number of ways 17 people can line up in a row for concert tickets.
Permutations. The order of the 17 people in line matters.
Outside a home, there is a 7-key keypad with letters A, B, C, D, E, F, and G can be used to open the garage if the correct seven-letter code is entered. Each key may be used only once. How many codes are possible?
Since order is important and we cannot press a key repeatedly if we wish, there are 7 choices for the first letter, 6 choices for the second letter, 5 choices for the third letter, and so on until we have entered a seven-letter code. Recall that a permutation is an ordered arrangement of objects. The number of different permutations of n distinct objects is n!. n!= n x (n-1) x (n-2) xxx3x2x1 Calculate the number of different seven-letter codes. 7!=7x6x5x4x3x2x1=5040.
Suppose Bill is going to burn a compact disk (CD) that will contain 15 songs. In how many ways can Bill arrange the 15 songs on the CD?
Since the songs are distinct, no song can be repeated on the CD, and order is important, you should count permutations. Use formula n!=nx (n-1) x (n-2)xxx3x2x1 15!=15x14x13x12x11x10x9x8x7x6x5x4x3x2x1=1,307,674,368,000. There are 1,307,674,368,000 ways.
Space shuttle astronauts each consume an average of 3000 calories per day. One meal normally consists of a main dish, a vegetable dish, and two different desserts. The astronauts can choose from 11 main dishes, 9 vegetable dishes, and 14 desserts. How many different meals are possible?
The fundamental counting principle can be used to find the number of ways two or more events can occur in sequence. In the given problem one meal consists of a main dish, a vegetable dish, and dessert. Thus, the number or events is 3. First determine n, the number of ways astronauts can choose a main dish. n=11 Now determine v, the number of ways astronauts can choose a vegetable dish. v=9 To find d, the number of ways astronauts can choose two different desserts, notice, that it is equal to the number of combinations of 2 desserts selected from a group of 14 desserts. d=14c2 Calculate the number of combinations. 14c2=14!/(14-2)!2! =14x13x12!/2x12! =91 The possible number of different meals, m, is found using the fundamental counting principle. m=NxVxD m=11x9x91=9009 There are 9009 ways.
When orange(RY) and red(RR) flowers are crossed, there are four equally likely possible outcomes for the genetic makeup of the offspring: red(RR), orange(RY), orange(YR), and red(RR). If orange(RY) and red(RR) snapdragons are crossed, what is the probability that the offspring will be (a) orange, (b) red?
The total number of possible outcomes in the sample space is 4. (a) If orange(RY) and red(RR) snapdragons are crossed, the flowers will be orange when the genetic makeup is RY or YR. Thus, the number of outcomes in which the offspring will be orange is 2. 2/4=0.5 (b) If orange(RY) and red(RR) snapdragons are crossed, the flowers will be red only when the genetic makeup is RR. Thus, the number of outcomes in which the offspring will be red is 2. 2/4=0.5
The table below shows the results of a survey in which 142 men and 146 women workers ages 25 to 64 were asked if they have at least one month's income set aside for emergencies. Complete parts (a) through (d).
(a) Find the probability that a randomly selected worker has one month's income or more set aside for emergencies. Take total number of people surveyed and divide by results of one month's income or more. 139/288=0.483 (b) Given that a randomly selected worker is a male, find the probability that the worker has less than one month's income. Take total number of males surveyed and divide by less than one months income. 65/142=0.458 (c) Given that a randomly selected worker has one month's income or more, find the probability that the worker is a female. Take amount of women who answered one month's income or more and divide by total who answered one month's income or more. 62/139= 0.446 (d) Are the events "having less than one month's income saved" and "being male" independent or dependent? Dependent.
Determine which numbers could not be used to represent the probability of an event.
-1.5, because probability values cannot be less than 0. 64/25, because probability values cannot be greater than 1.
