Exam 3: Probability

A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, The club president would like to know how many members regularly use each facility. A survey of The membership indicates that 57% regularly use the golf course, 48% regularly use the tennis Courts, and 9% use both of these facilities regularly. Given that a randomly selected member uses The tennis courts regularly, find the probability that they also use the golf course regularly.

A financial advisor has recommended three high-risk high-yield investments and four low-risk low-yield investments to one of her clients. In how many ways can the client select one of each Type of investment for his portfolio?

Suppose that an experiment has five sample points, $E _ { 1 } , E _ { 2 } , E _ { 3 } , E _ { 4 } , E _ { 5 }$ , and that $P \left( E _ { 1 } \right) = .2$ , $P \left( E _ { 2 } \right) = .3 , P \left( E _ { 3 } \right) = .1 , P \left( E _ { 4 } \right) = .1$ , and $P \left( E _ { 5 } \right) = .3$ . If the events $A$ and $B$ are defined as $A = \left\{ E _ { 1 } , E _ { 2 } , E _ { 3 } \right\}$ and $B = \left\{ E _ { 2 } , E _ { 3 } , E _ { 4 } \right\}$ find $P ( A \cap B )$ .

An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. Assuming that each of the numbers between 1 and 10 is equally likely To be chosen, find P(E).

A bag of candy was opened and the number of pieces was counted. The results are shown in the table below: Color Number Red 25 Brown 20 Green 20 Blue 15 Yellow 10 Orange 10 Find the probability that a randomly selected piece is either yellow or orange in color.

A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic)and their year in college (freshman, sophomore, junior, or senior). The results are Shown in the table below. Which of the following events listed would be considered mutually exclusive events?

At a certain university, one out of every 20 students is enrolled in a statistics course. If one student at the university is chosen at random, what is the probability that the student is enrolled in a Statistics course?

Suppose that for a certain experiment P(A)= .8 and P(B)= .9. Use the Additive Rule to explain why the events A and B can not be mutually exclusive.

A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in the state capital. Five hundred questionnaires were returned. Suppose an experiment consists of Randomly selecting one of the returned questionnaires. Consider the events: A: {The home is constructed of brick} B: {The home is more than 30 years old} D: {The home is heated with oil} Which of the following describes the event $B \cup D ^ { C }$ ?

If $P ( A \mid B ) = 0$ and $P ( A ) \neq 0$ , then which statement is false?

Fill in the blank. A(n)______ is a process that leads to a single outcome that cannot be predicted with certainty.

The table displays the probabilities for each of the outcomes when three fair coins are tossed and the number of heads is counted. Find the probability that the number of heads on a single toss of The three coins is at most 2. Outcome 0 1 2 3 Probability .125 .375 .375 .125

A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. It further estimates that 39 out of every 100 of its online customers is a man who does not live within 50 miles of one of its physical stores. Using this estimate, what is the probability that a randomly selected online customer is a man given that the customer does not live within 50 miles of a physical store?

A basketball player has an 80% chance of making the first free-throw he shoots. If he makes the first free-throw shot, then he has a 90% chance of making the second free-throw he shoots. If he Misses the first free-throw shot, then he only has a 70% chance of making the second free-throw He shoots. Suppose this player has been awarded two free-throw shots. Find the probability that He makes at least one of the two shots.

Find the numerical value. -A panel of coaches ranks the high school football teams in a particular state each week. The panel unanimously agrees on which five teams should comprise the top five but not on the order. Riverside High is among the top five. If the ranking of the top five is random, what is that Probability that Riverside High will be ranked first?

Each manager of a Fortune 500 company was rated as being either a good, fair, or poor manager by his/her boss. The managerʹs educational background was also noted. The data appear below: Educational Background Manager Rating H. S. Degree Some College College Degree Master's or Ph.D. Total Good 1 2 21 15 39 Fair 3 19 43 22 87 Poor 7 6 8 13 34 Total 11 27 72 50 160 What is the probability that a randomly chosen manager has earned at least one college degree?

On a certain statistics test, 20% of the students earned a score of 90 or above. It was also true that 20% of the male students earned a score of 90 or above. Are the events earning a score of 90 or above and being male independent? Explain.

A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. Using this estimate, what is the probability that a randomly Selected online customer does not live within 50 miles of a physical store?

The probability of a sample point is usually taken to be the relative frequency of the occurrence of the sample point in a very long series of repetitions of the experiment.

A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. Using this estimate, what is that probability that a a randomly Selected online customer lives within 50 miles of a physical store?