Exam 3: Probability

A machine has four components, $A , B , C$ , and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are $P ( \mathrm {~A} ) = P ( \mathrm {~B} ) = 0.97 , P ( \mathrm { C } ) = 0.9$ , and $P ( \mathrm { D } ) = 0.94$ . Find the probability that the machine works properly.

Classify the events as dependent or independent: Events A and B where P(A)= 0.8, P(B)= 0.5, and P(A andB)= 0.39.

Find the numerical value. -There are 10 players in a tennis tournament and five courts available for the first round. If players are randomly assigned to courts, what is the probability that the two most favored players are not Assigned to the same court?

If two events, A and B, are mutually exclusive, then $P ( A \text { and } B ) = P ( A ) \times P ( B ) \text {. }$

The table shows the political affiliations and types of jobs for workers in a particular state. Suppose a worker is selected at random within the state and the workerʹs political affiliation and type of job Are noted. Given that the worker is a Democrat, what is the probability that the worker has a white collar job.

A fair die is rolled one time. Let B be the event {1, 2, 5}. List the sample points in the event $B ^ { c } .$

A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the Probability that a green notepad is selected given that it is either blue or green.

Suppose the probability of an athlete taking a certain illegal steroid is 10%. A test has been developed to detect this type of steroid and will yield either a positive or negative result. Given That the athlete has taken this steroid, the probability of a positive test result is 0.995. Given that the Athlete has not taken this steroid, the probability of a negative test result is 0.992. Given that a Positive test result has been observed for an athlete, what is the probability that they have taken This steroid?

An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. List the sample points in E.

A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the sample space for the experiment.

A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below. What proportion of the employees are male or have been employed for less than 11 years?

If A and B,are independent events, then P(A)= P(B

If sample points A, B, C, and D are the only possible outcomes of an experiment, find the probability of D using the table below. Sample Point A B C D Probability 1/13 1/13 1/13

Suppose there are four dangerous military missions, each requiring one soldier. In how many different ways can 4 soldiers from a squadron of 100 be assigned to these four missions?

An event may contain sample points that are not in the original sample space of the experiment. For example, the experiment of rolling two dice has the following sample space: $\{ ( 1,1 ) , ( 1,2 ) , ( 1,3 ) , ( 1,4 ) , ( 1,5 ) , ( 1,6 ) , ( 2,1 ) , ( 2,2 ) , ( 2,3 ) , ( 2,4 ) , ( 2,5 ) , ( 2,6 ) \text {, }$ $( 3,1 ) , ( 3,2 ) , ( 3,3 ) , ( 3,4 ) , ( 3,5 ) , ( 3,6 ) , ( 4,1 ) , ( 4,2 ) , ( 4,3 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 )$ , $( 5,1 ) , ( 5,2 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,1 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) \}$ However, the event of rolling a sum of at least 11 on the two dice is {11, 12}.

Suppose that for a certain experiment P(A)= .32 and P(B)= .55. If A and B are independent events, find $P ( A \cap B ) .$

A certain game has a deck of numbered cards of various colors. The probability of drawing a green card from a well-shuffled deck is .25 and the probability of drawing a card numbered 3 is .1. Assuming that ʺgreenʺ and ʺ3ʺ are independent events, find the probability of drawing a green card numbered 3.

The following data represent the scores of 50 students on a statistics exam. Suppose that one of the 50 students is chosen at random and that studentʹs score is noted. 39 51 59 63 66 68 68 69 70 71 71 71 73 74 76 76 76 77 78 79 79 79 79 80 80 82 83 83 83 85 85 86 86 88 88 88 88 89 89 89 90 90 91 91 92 95 96 97 97 98 a. What is the probability that the student's score is 88? b. What is the probability that the student's score is less than 60? c. What is the probability that the student's score is between 70 and 79, inclusive?