Exam 11: General Rules of Probability

A roulette wheel has 38 slots in which the ball can land. Two of the slots are green, 18 are red, and 18 are black. The ball is equally likely to land in any slot. The roulette wheel is going to be spun twice, and the outcomes of the two spins are independent. The probability that the ball lands on black the first time and on green the second time is:

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. We may conclude that:

In a particular game, a six-sided fair die is tossed. If the number of spots showing is six, you win $6; if the number of spots showing is five, you win $3; if the number of spots showing is four, you win $2; and if the number of spots showing is three, you win $1. If the number of spots showing is one or two, you win nothing. You are going to play the game twice. The probability that you win something on each of the two plays of the game 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 40% choose jumping. Fifteen 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. If five students decide to join the team, what is the probability that at least one student joins the dressage team?

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 is fed more than 50% alfalfa, given that it has enteroliths, is:

A roulette wheel has 38 slots in which the ball can land. Two of the slots are green, 18 are red, and 18 are black. The ball is equally likely to land in any slot. The roulette wheel is going to be spun twice, and the outcomes of the two spins are independent. The probability that the ball lands on red at least once is:

Students at a local university have the option of taking freshman seminars during their first year in college. A survey of the freshmen revealed the following: Among the social science majors, 50% chose to take a freshman seminar; among the humanities majors, 65% chose to take a freshman seminar; and among the physical science majors, it was 30%. Freshmen make up 32% of undergraduates. The probability of taking a freshman seminar, if a student is a science major, 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 25 to 34 years old is:

Event A occurs with probability 0.2. Event B occurs with probability 0.9. Events A and B:

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 conditional probability that a student likes dubstep, given that he or she likes trance music, 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. All of the outcomes counted in this table are:

The following table gives the sex and age group of college students at a Midwestern university. A student is to be selected at random. Given that the selected student is female, the conditional probability that she is 25 to 34 years old is: