Exam 11: General Rules of Probability

A system has two components that operate in parallel, as shown in the following diagram. Because the components operate in parallel, at least one of the components must function properly if the system is to function properly. The probability of failure for components 1 and 2, during one period of operation, is 0.2 and 0.03, respectively. Let F1 denote the event that component 1 fails during one period of operation and F2 denote the event that component 2 fails during one period of operation. The component failures are independent. The event corresponding to the above system functioning properly during one period of operation is:

Veterinarians suspect that enteroliths (calcifications in the gut of horses) are related to diet-in particular, alfalfa. To investigate this suspicion, a group of veterinarians collected information on the diet of horses and whether the horses developed enteroliths. The table below displays the findings (a case is a horse with enteroliths, a control is without enteroliths). The probability that a randomly selected horse has enteroliths, given that it is fed more than 50% alfalfa, is:

Rolling a fair six-sided die three times is an example of:

A system has two components that operate in parallel, as shown in the following diagram. Because the components operate in parallel, at least one of the components must function properly if the system is to function properly. The probability of failure for components 1 and 2, during one period of operation, is 0.2 and 0.03, respectively. Let F1 denote the event that component 1 fails during one period of operation and F2 denote the event that component 2 fails during one period of operation. The component failures are independent. The probability that the system fails during one period of operation is closest to:

University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A student advisor needs to know the probability a newly admitted student is interested in such a program, so that the student can be properly advised. A study of previous years finds that the probability a student gets a Bachelor of Science degree is P(Science) = 0.3 and the probability a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The probability of getting a Bachelor of Science degree, given that a student is getting a Bachelor of Arts degree, is given by P(Science | Arts) = 0.3. The probability that a student will get no degree is:

In the Virginia instant lottery, there are 10 different $5 Scratcher games. Your favorite, "Hit the Jackpot," is advertised to have a 1-in-4.37 chance of winning, and a 1-in-664,457 chance of hitting the top prize of $200,000. All of the seven top prizes are still available. If you buy five of these tickets and outcomes are independent, the probability that you win all five times is:

A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The proportion of students that like trance music but not dubstep is:

A stack of four cards contains two red cards and two black cards. I select two cards, one at a time, and do not replace the first card selected before selecting the second card. Consider the events: A = the first card selected is red. B = the second card selected is red. The events A and B are:

A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The proportion of students that like neither trance music nor dubstep is:

Spelling mistakes in a text are either "nonword errors" or "word errors." A nonword error produces a string of letters that is not a word, such as "the" typed as "teh." Word errors produce the wrong word, such as "loose" typed as "lose." Nonword errors make up 25% of all errors. A human proofreader will catch 80% of nonword errors and 50% of word errors. Of all the errors that the proofreader catches, what percent are word errors?

University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A student advisor needs to know the probability a newly admitted student is interested in such a program, so that the student can be properly advised. A study of previous years finds that the probability a student gets a Bachelor of Science degree is P(Science) = 0.3 and the probability a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The study also shows that the probability a student gets no degree is P(no) = 0.2. The probability a student gets a Bachelor of Arts degree or a Bachelor of Science degree is:

Veterinarians suspect that enteroliths (calcifications in the gut of horses) are related to diet-in particular, alfalfa. To investigate this suspicion, a group of veterinarians collected information on the diet of horses and whether the horses developed enteroliths. The table below displays the findings (a case is a horse with enteroliths, a control is without enteroliths). The probability that a randomly selected horse gets more than 50% alfalfa is:

A group of freshmen at a local university consider joining the equestrian team. Thirty-five percent of students choose Western riding, 45% choose dressage, and 50% choose jumping. Twenty percent choose both dressage and jumping, while 10% choose Western and dressage. No one chooses Western and jumping. There are no horses suitable for two styles, and each student is assigned to one horse. What is the probability that a student chooses neither dressage nor Western riding?

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. The conditional probability of B, given A, is:

A system has two components that operate in parallel, as shown in the following diagram. Because the components operate in parallel, at least one of the components must function properly if the system is to function properly. The probability of failure for components 1 and 2, during one period of operation, is 0.2 and 0.03, respectively. Let F1 denote the event that component 1 fails during one period of operation and F2 denote the event that component 2 fails during one period of operation. The component failures are independent. The event corresponding to the above system failing during one period of operation is:

University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A student advisor needs to know the probability a newly admitted student is interested in such a program, so that the student can be properly advised. A study of previous years finds that the probability a student gets a Bachelor of Science degree is P(Science) = 0.3 and the probability a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The study also shows that the probability a student gets no degree is P(no) = 0.2. The probability a student gets a Bachelor of Arts and Science degree is:

University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A student advisor needs to know the probability a newly admitted student is interested in such a program, so that the student can be properly advised. A study of previous years finds that the probability a student gets a Bachelor of Science degree is P(Science) = 0.30 and the probability a student gets a Bachelor of Arts degree is P(Arts) = 0.60. If getting a Bachelor of Science degree is independent of getting a Bachelor of Arts degree, the probability of getting a Bachelor of Arts and Science degree is:

The following table gives the sex and age group of college students at a Midwestern university. A student is to be selected at random. The probability that the selected student is a female who is 15 to 17 years old is:

In the Virginia instant lottery, there are 10 different $5 Scratcher games. Your favorite, "Hit the Jackpot," is advertised to have a 1-in-4.37 chance of winning, and a 1-in-664,457 chance of hitting the top prize of $200,000. All of the seven top prizes are still available. If you buy five of these tickets and outcomes are independent, the probability that you lose all five times is:

University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A student advisor needs to know the probability a newly admitted student is interested in such a program, so that the student can be properly advised. A study of previous years finds that the probability a student gets a Bachelor of Science degree is P(Science) = 0.3 and the probability a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The study also shows that the probability a student gets no degree is P(no) = 0.2. Some probability calculations show the probability of getting a Bachelor of Arts and Science degree to be P(Arts & Science) = 0.1. Given this result, we conclude that: