Intro to Stats MCCC Ch. 4 – Flashcards

If A denotes some event, what does (complement of A) denote? If P(A)=0.003, what is the value of P(complement of A)? If P(A)=0.003, is (complement of A) unusual? a. What does (complement of A) denote? b. If P(A)=0.003, what is the value of P(complement of A)? c. If P(A)=0.003, is (complement of A) unusual?

Assume that 1200 births are randomly selected and exactly 608 of the births are girls. Use subjective judgment to determine whether the given outcome is unlikely, and also determine whether it is unusual in the sense that the result is far from what is typically expected. a. Determine whether exactly 608 girls out of 1200 randomly selected births is unlikely. b. Determine whether exactly 608 girls out of 1200 randomly selected births is unusual.

In a certain weather forecast, the chance of a thunderstorm is stated as 17%. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is ---

To the right are the outcomes that are possible when a couple has three children. Refer to that list, and find the probability of each event. boy- boy- boy boy- boy- girl boy - girl- boy boy- girl- girl girl- boy- boy girl- boy- girl girl- girl- boy girl- girl- girl a. What is the probability of exactly one girl out of three children? b. What is the probability of exactly 0 boys out of three children? c. What is the probability of exactly 3 girls out of three children?

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 odd number. (In roulette, 0 and 00 are neither odd nor even.) a. What is the probability of winning? b. What are the actual odds against winning? c. When you bet that the outcome is an odd number, the payoff odds are 1:1. How much profit do you make if you bet $10 and win? d. How much profit should you make on the $10 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning?

The ------ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.

What is wrong with the expression P(A) + P(mean of A) = 0.5?

Decide whether the following two events are disjoint. 1. Electing a president of the United States. 2. Electing a female candidate.

A research center poll showed that 80% 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?

The following data summarizes results from 1000 pre-employment drug screening tests. IF one of the test subjects is randomly selected, find the probability that the subject had a positive test result or a negative test result. Positive Negative Subject Uses Drugs 72 6 Subject Is Not a Drug User 82 840 P(subject had a positive test result or a negative test result) =

When using the ----- always be careful to avoid double-counting outcomes.

Describe what the notation P(B|A) represents.

For the given pair of events A and B, complete parts (a) and (b) below. A: When a page is randomly selected and ripped from a 12-page document and destroyed, it is page 4. B: When a different page is randomly selected and ripped from the document, it is page 9. a. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.) b. Find P(A and B), the probability that events A and B both occur.

Refer to the table below. Given that 2 of the 108 subjects are randomly selected, compare parts (a) and (b). Group ------------------------------------------------------------------------------------ O A B AB Type Rh + 36 31 13 13 Rh- 7 6 1 1 a. Assume that the selections are made with replacement. What is the probability that the 2 selected subjects are both group B and type Rh+? b. Assume the selections are made without replacement. What is the probability that the 2 selected subjects are both groups B and type Rh+?

With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. A company has just manufactured 1667 CDs, and 670 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted? Does this outcome suggest that the entire batch consists of good CDs? Why or why not? a. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted? b. Does the result in (a) suggest that the entire batch consists of good CDs? Why or why not?

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 19.3% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? c. What is the probability of not being awakened if the student uses three independent alarm clocks? d. Do the second and third alarm clocks result in greatly improved reliability?

Which word is associated with multiplication when computing probabilities?

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.

Determine the written description of the complement of the given item. When seven athletes are tested for a certain ability, at least one of them tests negative.

If a couple plans to have 7 children, what is the probability that there will be at least one girl? Assume boys and girls are equally likely. Is that probability high enough for the couple to be very confident that they will get at least one girl in 7 children? a. The probability is? b. Can the couple be very confident that they will have at least one girl?

Find the probability of a couple having a baby boy when their fifth child is born, given that the first four children were all boys. Assume boys and girls are equally likely. Is the result the same as the probability of getting all boys among five children? a. The probability is? b. Is this result the same as the probability of getting all boys among five children?

The probability of a randomly selected car crashing during a year in a certain country is 0.0471. If a family has four cars, find the probability that at least one of them has a car crash during a year. Is there any reason why the probability might be wrong? a. The probability that at least one of them has a crash during the year is? b. Is there a reason why the probability might be wrong?

The data represents the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative, given that he or she did not have the disease. The individual actually had the disease Yes No Positive 143 23 ------------------------------------------------------- Negative 14 120 The probability is approximately?

The table below displays results from experiments with polygraph instruments. Find P(subject lied | negative test result). Compare this result with the probability of selecting a subject with a negative test result, given that the subject lied. Are P(subject lied | negative test result) and P(negative test result | subject lied) equal? Did the Subject Actually Lie? No (Did not lie) Yes (Lied) Positive Results 13 44 Negative Results 31 8 a. P(subject lied | negative test result) = b. Find the probability of selecting a subject with a negative test result, given that the subject lied. P(negative test result | subject lied) = c. Compare the two values. Are they equal?

The accompanying table displays results from experiments with polygraph instruments. a. Find P(subject told the truth | negative test result). b. Find P(negative test result | subject told the truth). c. Compare the results from parts a. and b. Are they equal? Did the Subject Actually Lie? No (did not lie) Yes (lied) Positive Results 13 44 Negative Results 33 9 a. P(subject told the truth | negative test result) = b. Find the probability of selecting a subject with a negative test result, given that the subject to the truth. P(negative test result | subject told the truth) = c. Compare the two values. Are they equal?

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. Did the Subject Actually Lie? No (did not lie) Yes (lied) Positive Results 18 45 Negative Results 30 11 The probability is?

Identical twins come from a single egg that split into two embryos, and fraternal twins are from separate fertilized eggs. Also, identical twins must be of the same sex and sexes are equally likely, and sexes of fraternal twins are equally likely. Use the data to complete parts (a) and (b) below. Sexes of Twins boy/boy boy/girl girl/boy girl/girl Identical Twins 9 0 0 9 Fraternal Twins 8 8 8 8 a. After having a sonogram, a pregnant woman learns that she will have twins. What is the probability that she will have identical twins? b. After studying the sonogram more closely, the physician tells the pregnant woman that she will give birth to twin boys. What is the probability that she will have identical twins? That is, find the probability of identical twins given that the twins consist of two boys.

Assume that there is a 11% 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 four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

"At least one" is equivalent to -------

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 this trifecta involve combinations are permutations? Explain.

A thief steals an ATM card and must randomly guess the correct three-digit code from a 7-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try? a. The number of possible codes is? b. The probability that the correct code is given on the first try is?

If you know the names of the remaining seven 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? P(selecting the correct spelling bee order) =

A fan of country music plans to make a custom CD with 12 of her 26 favorite songs. How many different combinations of 12 songs are possible? Is it practical to make a different CD for each possible combination? a. How many different combinations of 12 songs are possible? b. Is it practical to make a different CD for each possible combination?