Exam 3: Probability

The data show the total number of medals (gold, silver, and bronze)won by each country winning at least one gold medal in the Winter Olympics. 1 2 3 3 4 9 9 11 11 11 14 14 19 22 23 24 25 29 Suppose that one of the countries represented is selected at random and the total number of medals won by that country is noted. What is the probability that the country won at least 25 medals given that the country did not win fewer than 10 medals?

Suppose a basketball player is an excellent free throw shooter and makes 92% of his free throws (i.e., he has a 92% chance of making a single free throw). Assume that free throw shots are Independent of one another. Find the probability that the player misses three consecutive free Throws.

Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown Below: Given that an accident involved multiple vehicles, what is the probability that it involved alcohol?

The table shows the number of each type of book found at an online auction site during a recent search. Suppose that Juanita randomly chose one book to bid on and then noted its type. a. List the sample points for this experiment. b. Find the probability of each sample point. c. What is the probability that the book was nonfiction or educational?

For all events A and B, the conditional probabilities $P ( A \mid B ) \text { and } P ( B \mid A )$ are equal.

A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 6} B: {At least one of the numbers 3} a. Identify the sample points in the event $A \cup B$ . b. Identify the sample points in the event $A \cap B$ . c. Find $P ( A \cup B )$ . d. Find $P ( A \cap B )$ .

The outcome of an experiment is the number of resulting heads when a nickel and a dime are flipped simultaneously. What is the sample space for this experiment?

A rental company offers 12 choices of table linens, three choices of china, two choices of flatware, and three choices of stemware. In how many ways can a customer choose one of each to set the Tables for a wedding reception?

In a particular town, 20% of the homes have monitored security systems. If an alarm is triggered, the security system company will contact the local police to alert them of the alarm. Of all the Alarm calls that the local police receive, they only have the manpower to answer 30% of the calls. Suppose we randomly sample one home that was broken into over the last month from this town. What is the probability that this home has a monitored security system and that the police Answered the alarm call?

For two events, $A$ and $B , P ( A ) = .6 , P ( B ) = .8$ , and $P ( A \mid B ) = .5$ . Find $P ( A \cap B )$ .

If events A and B are not mutually exclusive, then it is possible that $P ( A ) + P ( B ) > 1$

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. Given that you know the selected student is in the senior class, find the probability they drive a domestic automobile.

You toss a coin five times. What is the probability of getting heads on the first two tosses and tails on the next three tosses?

A hospital reports that two patients have been admitted who have contracted Crohnʹs disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of The disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 Dies, etc.). Simple Events Probabilities SS 0.55 SD 0.20 DS 0.16 DD 0.09 Find the probability that both patients survive.

The accompanying Venn diagram describes the sample space of a particular experiment and events $A$ and $B$ . Suppose $P ( 1 ) = P ( 2 ) = P ( 3 ) = P ( 4 ) = \frac { 1 } { 16 }$ and $P ( 5 ) = P ( 6 ) = P ( 7 ) = P ( 8 ) =$ $P ( 9 ) = P ( 10 ) = \frac { 1 } { 8 }$ . Find $P ( A )$ and $P ( B )$

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. Find the probability the worker is not an Independent.

The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified. Events $A$ and $B$ are defined as follows. A:{Convertible, SUV, Van $\}$ B : Fewer than 10,000 of the type of car were sold in June } a. Identify the sample points in the event $A \cup B$ . b. Identify the sample points in the event $A \cap B$ . c. Find $P ( A \cup B )$ . d. Find $P ( A \cap B )$ .

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 68% regularly use the golf course, 47% regularly use the tennis Courts, and 3% use neither of these facilities regularly. What is the probability that a member Regularly uses at least one of the golf or tennis facilities?

Fill in the blank. The __________ is the collection of all the sample points in an experiment.

A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The number is less than 7} Which expression represents the event that the number is both even and less than 7?