Statistics Chapter 4 Review
Twenty of the 100 digital video recorders(DVRs) in an inventory are known to be defective. What is the probability that a randomly selected item isdefective?
.20%
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 16.7%
0.167 0.027890= 0.167 squared 0.004660= 0.167 cubed D. Yes, because total malfunction would not be impossible, but it would be unlikely.
A research center poll showed that 81% 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
0.19
Eleven of the 50 digital video recorders(DVRs) in an inventory are known to be defective. What is the probability that a randomly selected item isdefective?
0.22
Testing for a disease can be made more efficient by combining samples. If the samples from six people are combined and the mixture tests negative, then all six samples are negative. On the other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.05,find the probability of a positive result for six samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary?
0.265 The probability is not low, so further testing of the individual samples will frequently be a necessary event.
In a genetics experiment on peas, one sample of offspring contained 409 green peas and 504 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 34 that was expected?
0.448, no it is not close
The table below displays results from experiments with polygraph instruments. Find the positive predictive value for the test. That is, find the probability that the subject lied, given that the test yields a positive result.
0.683
For a certain casino slot machine, the odds in favor of a win are given as 83 to 17. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
0.83
In a test of a sex-selection technique, results consisted of 224 female babies and 14 male babies. Based on this result, what is the probability of a female being born to a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
0.941, yes
Assume that there is a 7% 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? b. If copies of all your computer data are stored on three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
0.9951= 1-0.0049 0.999657=1-0.000343
Winning the jackpot in a particular lottery requires that you select the correct four numbers between 1 and 59 and, in a separate drawing, you must also select the correct single number between 1 and 39. Find the probability of winning the jackpot.
1/17749914 4/59 3/58 2/57 1/56 1/39
On their first date, Kelly asks Mike to guess the date of her birth, not including the year. Complete parts a through c below.
1/365 Yes, it is unlikely for Mike to guess correctly on his first try, as the probability of a correct guess is very low. Already knew, very low
You want to obtain cash by using an ATM, but it's dark and you can't see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first. Complete parts (a) through (c)
1/4 3/16 This is a trick question. There is no finite number of attempts, because it is possible to get the wrong position every time.
A modified roulette wheel has 32 slots. One slot is 0, another is 00, and the others are numbered 1 through 30, respectively. You are placing a bet that the outcome is an even number. (In roulette, 0 and 00 are neither odd nor even.)
15/32 17:15 17 19.27$
If radio station call letters must begin with either K or W and must include either two or three additional letters, how many different possibilities are there?
36504
Find the probability that when a couple has three children, at least one of them is a boy. (Assume that boys and girls are equally likely.)
7/8
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.
Let A be the event of rolling a die and getting 6, and let B be the event of tossing a coin and getting heads. When finding the probability that events A and B both occur, which formula applies?
P(A and B)= P(A)P(B)
Two different days of the week are randomly selected without replacement. Let W be the event of selecting Wednesday on the first selection, and let F be the event of selecting Friday on the second selection. When finding the probability that events W and F both occur, which formula applies?
P(A and B)=P(A)P(BIA)
In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts (a) through (c) below.
The probability is 0.675 0.3250. A student given four quarters is more likely to have spent the money. Your answer is correct.
A county clerk was supposed to use randomness to assign the order in which candidates' names appeared on voting ballots. Among 38 different ballots, Democratic candidate names were placed on the first line 35 times. The probability of a result that high is 0.000000033389. Assuming randomness was used, is the result of 35 Democratic candidate names being placed on the first line significantly low, significantly high, or neither?
The probability of a result of 35, which is 0.000000033389, is less than or equal to 0.05. The result, 3538, is much higher than what is expected with randomness. The result of 35 is significantly high.
Order Accurate 332 278 237 149 Order Not Accurate 31 57 39 15 If one order is selected, find the probability of getting an order from Restaurant A or an order that is accurate. Are the events of selecting an order from Restaurant A and selecting an accurate order disjoint events?
The probability of getting an order from Restaurant A or an order that is accurate is 0.903 P The events are not disjoint because it is possible to receive an accurate order from Restaurant A.
If one order is selected, find the probability of getting an order that is not accurate or is from Restaurant C. Are the events of selecting an order that is not accurate and selecting an order from Restaurant C disjoint events?
The probability of getting an order from Restaurant C or an order that is not accurate is 0.3510 The events are not disjoint because it is possible to receive an inaccurate order from Restaurant C.
When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P(M|B) represent? Is P(M|B) the same as P(B|M)?
The probability of getting a male, given that someone with blue eyes has been selected. No, because P(B|M) represents the probability of getting someone with blue eyes, given that a male has been selected.
Let event A=subject 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
In a particular survey of internet users, 3603 respondents say that they use social networking sites and 1457 respondents say that they do not use social networking sites. What is the probability that a randomly selected person uses a social networking site? Does that result suggest that it is likely (with a probability of 0.5 or greater) for someone to use social networking sites?
Yes,because the probability of a respondent using social media is greater than 0.5.
Refer to the figure below in which surge protectors p and q are used to protect an expensive high-definition television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.97 probability of working correctly when a voltage surge occurs. Complete parts (a) through (c) below.
a. If the two surge protectors are arranged in series, what is the probability that a voltage surge will not damage the television? 0.99910 b. If the two surge protectors are arranged in parallel, what is the probability that a voltage surge will not damage the television? 0.9409 c. Which arrangement should be used for better protection? The series arrangement provides better protection because it has a higher probability of protection.
A modified roulette wheel has 44 slots. One slot is 0, another is 00, and the others are numbered 1 through 42 respectively. You are placing a bet that the outcome is an odd number. {In roulette, 0 and 00 are neither odd nor even}
a. the probability of einning is 21/44b. The actual odds against winning are....1-(21/44)= 23:21c. If you win, the payoff is $16d. 16×(23/21)= 17.52
When using the _______ always be careful to avoid double-counting outcomes.
addition rule
Each of two parents has the genotype red/brown, which consists of the pair of alleles that determine hair color, and each parent contributes one of those alleles to a child. Assume that if the child has at least one red allele, that color will dominate and the child's hair color will be red. a. List the different possible outcomes. Assume that these outcomes are equally likely. b. What is the probability that a child of these parents will have the brown/brown genotype? c. What is the probability that the child will have red hair color?
red/red, red/brown, brown/red, and brown/brown 0.25 0.75
The _______ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.
sample space
Let A denote the event of placing a $1 straight bet on a certain lottery and winning. Suppose that, for this particular lottery, there are 4,480 different ways that you can select the four digits (with repetition allowed) in this lottery, and only one of those four-digit numbers will be the winner. What is the value of P(A)? What is the value of P(A)?
P(A)=0.000220 What is the value of P(A)? P(A)=0.999780
