3.3 HW
The table below shows the results of a survey that asked 2861 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (d) (a) Find the probability that the person is frequently or occasionally involved in charity work. P(being frequently involved or being occasionally involved)=_ (b) Find the probability that the person is female or not involved in charity work at all. P(being female or not being involved)=_ (c) Find the probability that the person is male or frequently involved in charity work. P(being male or being frequently involved)=_ (d) Find the probability that the person is female or not frequently involved in charity work. P(being female or not being frequently involved)=_
(a) 0.460 (432/2861)+(885/2861)=0.460 (b) 0.763 ((1383/2861)+(1544/2861))-(745/2861)=0.763 (c) 0.589 ((1478/2861)+(432/2861))-(224/2861)=0.589 (d) 0.922 ((1383/2861)+(2429/2861))-(1175/2861)=0.922 885+1544=2429 430+745=1175
REDO The accompanying table shows the numbers of male and female students in a certain region who received bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts (a) through (c) below. (a) The student is male or received a degree in the field The probability is _ (b) The student is female or received a degree outside of the field The probability is _ (c) The student is not female or received a degree outside of the field The probability is _
(a) 0.531 ((791224/1753896)+(331835/1753896))-(190879/1753896)=0.531 (b) 0.891 ((962672/1753896)+(1422061/1753896))-(821716/1753896)=0.891 (c) 0.920 ((791224/1753896)+(1422061/1753896))-(600345/1753896)=0.920
A card is selected at random from a standard deck of 52 playing cards. Find the probability of each event. (a) Randomly selecting a heart or a 9 (b) Randomly selecting a black suit or a king (c) Randomly selecting a 3 or a face card (a) The probability of randomly selecting a red suit or a king is _ (b) The probability of randomly selecting a spade or a 5 is _ (c) The probability of randomly selecting a 4 or a face card is _
(a) 0.538 ((26/52)+(4/52))-(2/52)=0.538 (b) 0.308 ((13/52)+(4/52))-(1/52)=0.308 (c) 0.308 (4/52)+(12/52)=0.308
The responses of 1466 voters to a survey about the way the media conducted themselves in a recent political campaign are shown in the accompanying Pareto chart. Find the probability of each event listed in parts (a) through (d) below. (a) Randomly selecting a person from the sample who did not give the media an A or a B The probability is _ (b) Randomly selecting a person from the sample who gave the media a grade better than a D The probability is _ (c) Randomly selecting a person from the sample who gave the media a D or an F The probability is _ (d) Randomly selecting a person from the sample who gave the media a C or a D The probability is _
(a) 0.769 (567+314+247)=1128/1466=0.769 (b) 0.399 (338+247)=585/1466=0.399 (c) 0.601 (567+314)=881/1466=0.601 (d) 0.383 (314+247)=561/1466=0.383
The estimated percent distribution of a certain country's population for 2025 is shown in the accompanying pie chart. Find the probability of each event listed in parts (a) through (d) below. (a) Randomly selecting someone who is under 5 years old The probability is _% (b) Randomly selecting someone who is 45 years old or over The probability is _% (c) Randomly selecting someone who is not 65 years old or over The probability is _% (d) Randomly selecting someone who is between 20 and 34 years old The probability is _%
(a) 6.4 (b) 44.1 25.3+11.1+7.7=44.1 (c) 81.1 6.4+12.5+5.1+6.5+12.7+12.6+25.3=81.1 (d) 19.2 6.5+12.7=19.2
A physics class has 50 students. Of these, 17 students are physics majors and a total of 16 students are minoring in math, including 4 students that are both majoring in physics and minoring in math. Find the probability that a randomly selected student is minoring in math or a physics major. The probability that a randomly selected student is minoring in math or a physics major is _
0.580 ((17/50)+(16/50))-(4/50)=0.580
In a group of 40 students, 17 are taking "Video Game History: Rise of a New Medium:, 16 are taking "Muppet Magic: Jim Henson's Art" and seven are taking both classes. Find the probability that a randomly selected student is taking "Video Game History" or "Muppet Magic." The probability that a randomly selected student is taking "Video Game History" or "Muppet Magic" is _
0.650 ((17/40)+(16/40))-(7/40)=0.650
There is a group of 40 college instructors. Of these, 12 teach Mathematics and 18 are female. Of those who teach Mathematics, three are female. Find the probability that a randomly selected college instructors is female or teaches Mathematics. The probability that a randomly selected college instructors is female or teaches Mathematics is _
0.675 ((12/40)+(18/40))-(3/40)=0.675
Of the cartons produced by a company, 10% have a puncture, 7% have a smashed corner, and 1.3% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner _%
15.7 (10+7)-1.3=15.7
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. Choose the correct answer below. a. True b. False. If two events are mutually exclusive, they have every outcome in common c. False. If two events are mutually exclusive, they have some outcomes in common
a. True
Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning. The events _ mutually exclusive, since there _ and _
are not; is at least 1 presidential candidate who had proposed tax reductions; lost the election
Determine whether the following events are mutually exclusive. Explain your reasoning. Event A: Randomly select a female history major Event B: Randomly select a history major who is 19 years old These events _ mutually exclusive, since _
are not; it is possible to select a female history major who is 19 years old
Determine whether the following events are mutually exclusive. Explain your reasoning. Event A: Randomly select a voter who legally voted for the President in Delaware Event B: Randomly select a voter who legally voted for the President in Pennsylvania These events _ mutually exclusive, since it _ possible for a voter to both
are; is not; have
Determine whether the following statement is true or false. If it is false, explain why. The probability that event A or event B will occur is P(A or B)=P(A)+P(B)+P(A and B) Choose the correct answer below. a. False, the probability that A or B will occur is P(A or B)=P(A)•P(B) b. False, the probability that A or B will occur is P(A or B)=P(A)+P(B)−P(A and B) c. False, the probability that A or B will occur is P(A or B)=P(A)+P(B) d. True
b. False, the probability that A or B will occur is P(A or B)=P(A)+P(B)−P(A and B)
If two events are mutually exclusive, why is P(A and B)=0? Choose the correct answer below. a. P(A and B)=0 because A and B each have the same probability b. P(A and B)=0 because A and B are independent c. P(A and B)=0 because A and B cannot occur at the same time d. P(A and B)=0 because A and B are complements of each other
c. P(A and B)=0 because A and B cannot occur at the same time
