Exam 4: Probability and Counting Rules

A Karate club consists of 52 persons holding a black belt (highest rating), 69 persons holding a brown belt (middle rating), and 83 persons holding a purple belt (lowest Rating). What is the probability that a randomly-selected club member holds a black belt?

In the Happy Hilltop Health Home, 10% of the residents play shuffleboard, 35% of the residents play poker, and 15% of the residents garden. If 5% of the residents play poker And garden, find the probability that a resident plays poker, given that they also garden.

For the event described below, which of the following represents the complement of the event. A sample of 318 software DVDs was selected. Fewer than 44 of these were Defective.

A lot of 1000 components contains 250 that are defective. Two components are drawn at random and tested. Let $A$ be the event that the first component drawn is defective, and let $B$ be the event that the second component drawn is defective. Find $P ( B \mid A )$ .

So far this season, the university's football team has executed 155 running plays, 143 passing plays, and 19 "trick" plays. What is the probability that the team will not execute A trick play?

In a recent semester at a local university, 500 students enrolled in both General Chemistry and Calculus I. Of these students, 66 received an A in general chemistry, 73 Received an A in calculus, and 33 received an A in both general chemistry and calculus. Find the probability that a randomly chosen student received an A in general chemistry or calculus Or both.

For this year's mayoral election, voter dissatisfaction is very high. In a survey of 500 likely voters, 240 said they planned to write in an independent candidate rather than vote for the Democrat or Republican candidate for mayor. Estimate the percentage of voters who plan to write in an independent candidate?

For the event described below, which of the following represents the complement of the event. A sample of 351 software DVDs was selected. Exactly 29 of these were defective.

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the Probability (as a reduced fraction) that at least one answer is "A". [Hint: List all the Outcomes of the sample space first.]

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let C be the event that at least two doors are unlocked. List the outcomes of "L" designate "locked" and U" designate "unlocked".]

A Karate club consists of 41 persons holding a black belt (highest rating), 59 persons holding a brown belt (middle rating), and 73 persons holding a purple belt (lowest Rating). What is the probability that a randomly-selected club member holds a brown belt Or a purple belt?

A certain system has two components. There are 6 different models of the first component and 11 different models of the second. Any first component can be paired With any second component. A salesman must select 2 of the first component and 3 of The second to take on a sales call. How many different sets of components can the Salesman take?

On a TV game show, a contestant is shown 8 products from a grocery store and is asked to choose the three least-expensive items in the set. The three chosen items need not be In any particular order. In how many ways can the contestant choose the three items?

What type of probability uses a knowledge of sample spaces as opposed to experiments to determine the numerical probability that an event will occur?

There are 28,446 undergraduate students enrolled at a certain university. The age distribut is as follows: Age Range Number 13-14 5 15-17 434 18-22 12,057 23-30 9256 31 and up 6694 Total 28,446 What is the probability that a student is less than 18 years old? n

Let $E$ be the event that a corn crop has an infestation of ear worms, and let $B$ be the event that a corn crop has an infestation of corn borers. Suppose that $P ( E ) = 0.24 , P ( B ) = 0.16$ , and $P ( E$ and $B ) = 0.13$ . Find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both.

Each of 5 students wishes to buy a particular textbook, but only 2 textbooks are available. How could one express the number of ways those textbooks could be Distributed among the students?

Two events are mutually exclusive if they cannot both occur.

An apartment building has the following distribution of apartments: bedroom 1st floor 3 1 1 2nd floor 1 3 2 3rd floor 1 4 1 If an apartment is selected at random, what is the probability that it is on the 2nd floor or has 2 bedrooms?

When the outcome of event A does not affect the probability of the outcome of a subsequent event B, then the events are said to be dependent.