Stat. Ch 4
A certain group of women have a 0.39% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
0.0039 1-0.0039 =0.9961 the probability is 0.9961
Assume that there is a 5% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
0.05 x 0.05 =0.025 subtract answer by 1 1-0.0025 =0.9975 Probability is 0.9975
In a genetics experiment on peas, one sample of offspring contained 350 green peas and 102 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was expected?
350+102 =452 350/452 =0.774 the probability of getting a green pea is approximately 0.774
A research center poll showed that 84% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?
Turn 84 into decimal 84/100 =0.88 1-0.88 =.16 the probability is .16
Among 5383 cases of heart pacemaker malfunctions, 410 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in 3 different pacemakers randomly selected from this batch of 5383 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted?
calculate the probability 410/5383 =0.076166 Then subtract answer by 1. 1-0.076166 =0.923834 There are 3 different pacemakers, so multiply 0.923834 by itself 3 times. =0.788 Probability is 0.788
In a certain weather forecast comma the chance of a thunderstorm is stated as 15%. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
To convert a percentage to a decimal number, remove the % symbol and divide by 100. 15/100 =0.15
When four basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. What is the probability that they shoot free throws in alphabetical order? Assume each player has a different name.
4*4*4*4 =24 the probability is 1/24
A thief steals an ATM card and must randomly guess the correct four-digit pin code from a 8-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
8*8*8*8 = 4096 number of possible codes 4096 probability is 1/4096
In horse racing, a trifecta is a bet that the first three finishers in a race are selected, and they are selected in the correct order. Does a trifecta involve combinations or permutations? Explain.
Because the order of the first three finishers does make a difference, the trifecta involves permutations.
a. What is the probability that the student's alarm clock will not work on the morning of an important final exam?
Convert the percentage into a decimal. 12.1/100 = 0.121 Probability is 0.121
If A denotes some event, what does Ā denote? If P(A) = 0.006, what is the value of P(Ā)?
Event Ā denotes the complement of event A, meaning that Ā consists of all outcomes in which event A does not occur.. so if p(a) - 0.006, the value of P(Ā) is 0.994. because 1-0.006 = 0.994
c. What is the probability of not being awakened if the student uses three independent alarm clocks?
Multiply 0.121 by itself 3 times. 0.121 x 0.121 x 0.121 =0.00177 Probability is 0.00177
A combination lock uses three numbers between 1 and 29 with repetition, and they must be selected in the correct sequence. Is the name of "combination lock" appropriate? Why or why not?
No, because the fundamental counting rule would be used to determine the total number of combinations.
In a certain country, the true probability of a baby being a boy is 0.509. Among the next six randomly selected births in the country, what is the probability that at least one of them is a girl?
Probability of boy is 0.509 There are six random births, so multiply 0.509 six times. 0.509 x 0.509 x 0.509 x 0.509 x 0.509 x 0.509 =0.017 then subtract answer by 1 1-0.017 = 0.983 Probability is 0.983
What does P(B|A) represent?
The probability of event B occurring after it is assumed that event A has already occurred
Let event A = is telling the truth and event B = polygraph test indicates that the subject is lying. Use your own words to translate the notation P(B|A) into a verbal statement
The probability that the polygraph indicates lying given that the subject is actually telling the truth.
Again let A = at least 1 hard drive works correctly. Using the same method as in part (a), find the probability of the complement of event A.
multiply 0.05 by itself 3 times 0.05 x 0.05 x 0.05 =0.000125 subtract answer by 1 1-0.000125 =0.999875 Probability is 0.999875
If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam?
multiply 0.121 by 0.121 0.121 x 0.121 =0.01464 Probability is 0.01464
c. What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates?
1/680
Seventeen of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability that a randomly selected item is defective?
17/100 =0.17 the probability is 0.17
Events that are _______ cannot occur at the same time.
Events that are disjoint cannot occur at the same time.
A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. After seeing the last four digits printed on a receipt, if you randomly select the other digits, what is the probability of getting the correct Social Security number of the person who was given the receipt?
10 numbers 0-9 can be used in ss number 4 numbers are known 10*10*10*10= 100000 probability is 1/100000
Winning the jackpot in a particular lottery requires that you select the correct four numbers between 1 and 49 and, in a separate drawing, you must also select the correct single number between 1 and 52. Find the probability of winning the jackpot.
this is a combination statcrunch: n=49 r=4 comb(49,4) =211875 statcrunch: n=52, r=1 comb(52,1) =52 211875 x 52 =11017552 probability is 1/11017552
b. How many different ways can the committee be appointed?
this is a combination, because there is no specific order statcrunch: n=17, r=3 comb(17, 3) =680 there are 680 different ways to appoint the committee
a. How many different ways can the officers be appointed?
this is a permutation bc the order is important, like a hierarchy statcrunch: n=17, r=4 perm(17, 4) =57120 there are 57120 different ways to appoint the officers
c. How many random selections are required to be absolute sure that the card works because it is inserted correctly?
this is a trick question
If you know the names of the remaining three students in the spelling bee, what is the probability of randomly selecting an order and getting the order that is used in the spelling bee?
three students 3!= 3x2x1 3x2x1=6 probability is 1/6
Among 500 randomly selected drivers in the 16 - 18 age bracket, 256 were in a car crash in the last year. If a driver in that age bracket is randomly selected, what is the approximate probability that he or she will be in a car crash during the next year? Is it unlikely for a driver in that age bracket to be involved in a car crash during a year?
the trial was repeated 500 times. divide 500 by the age bracket, which = 256 256/500 =0.512
a. What is the probability of selecting a random position and inserting the card with the result that the card is inserted correctly?
there are 4 ways to insert the card only 1 is correct so your odds are 1/4 =1/4
b. What is the probability of randomly selecting the card's position and finding that it is incorrectly inserted on the first attempt, but it is correctly inserted on the second attempt? (Assume that the same position used for the first attempt could also be used for the second attempt.)
there is a 3/4 chance of getting it wrong the first time there is a 1/3 chance of getting it right the second time 3/4 x 1/3 = 1/4
In a small private school, 5 students are randomly selected from 13 available students. What is the probability that they are the five youngest students?
this is a combination n=13, r=5 inset this into statcrunch, data, compute, expressions comb(13, 5) answer is 1287 probability is 1/1287
