Exam 3: Probability

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 0.53 SD 0.12 DS 0.17 DD 0.18 Find the probability that neither patient survives.

A music store has 8 male and 12 female employees. Suppose one employee is selected at random and the employeeʹs gender is observed. List the sample points for this experiment, and assign Probabilities to the sample points.

Determine the number of sample points in the sample space corresponding to the experiment of tossing a coin 6 times.

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: Suppose that one of the 400 accidents is chosen at random. What is the probability that the accident involved alcohol or a single car?

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: Suppose that one of the 400 accidents is chosen at random. What is the probability that the accident involved more than a single vehicle?

Kim submitted a list of 12 movies to an online movie rental company. The company will choose 3 of the movies and ship them to her. If all movies are equally likely to be chosen, what is the Probability that Kim will receive the three movies that she most wants to watch? Express the Probability as a fraction.

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 66% regularly use the golf course, 44% regularly use the tennis courts, and 17% use both of these facilities regularly. Find the probability that a randomly selected member uses the golf or tennis facilities regularly.

An insurance company looks at many factors when determining how much insurance will cost for a home. Two of the factors are listed below: A: {The homeʹs roof is less than 10 years old} B: {The home has a security system} In the words of the problem, define the event Bc.

Suppose you teach a class of twelve students that you wish to assign to three groups of four students each. In how many different ways can groups be made?

Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows. A: {Both chips are red} B : {At least one of the chips is blue} a. Identify the sample points in the event $A \cup B$ . b. Find $P ( A \cup B )$ .

At a certain university, 70% of the students own cars. However, only 45% of the residence hall students own cars. Are the events owning a car and living in a residence hall independent? Explain.

Based on past experience, Josh believes that the probability of catching a red snapper is .21 and the probability of catching a fish that weighs less than 5 pounds is .45. Is enough information available to find the probability of catching a red snapper or a fish that weighs less than 5 pounds? Explain. If possible, find the probability of catching a red snapper or a fish that weighs less than 5 pounds.

In how many ways can a manager choose 3 of his 8 employees to work overtime helping with inventory?

Which number could be the probability of an event that rarely occurs?

A group of 13 people is traveling in three vehicles. If 6 people ride in the van, 5 people ride in the car, and 2 people ride in the pickup, in how many different ways can the people be assigned to the vehicles?

The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Suppose that the die is rolled once. Let $A$ be the event that the number rolled is less than 4 , and let $B$ be the event that the number rolled is odd. Find $P ( A \cap B )$ .

A pair of fair dice is tossed. Events A and B are defined as follows. A: {The two numbers rolled are different} B: {At least one of the numbers is greater than 2} a. Identify the sample points in the event $A ^ { C }$ . b. Identify the sample points in the event $B ^ { C }$ . c. Identify the sample points in the event $A ^ { C } \cup B ^ { C }$ . d. Identify the sample points in the event $A ^ { C } \cap B ^ { C }$ . e. Find $P \left( A ^ { c } \cup B ^ { C } \right)$ . f. Find $P \left( A ^ { C } \cap B ^ { C } \right)$ .

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. Are the events, A - the Player makes the first shot, and B - the player makes the second shot, independent events?

Unions and intersections cannot be defined for more than two sets, so that $A \cup B \cup C$ and $A \cap B \cap C$ are meaningless.

Store Brand A fabric softener is among 10 brands being rated by a consumer group. If the group ranks the brands at random, what is the probability that Store Brand A fabric softener will be ranked first?