Exam 10: Introducing Probability

You have three cards, labeled 1, 2, and 3. You select two of the cards at random and note the numbers on the two cards. Let X be the sum of the two numbers labeled on the selected cards. Which of the following is the correct set of probabilities for X?

I toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair; that is, the probability of heads is 1/2 and the probability of tails is 1/2. This means that:

A geneticist developed a new type of pest-resistant walnuts. These walnuts produce 75% of pest-resistant walnut trees and 25% of susceptible (not resistant) trees when two resistant trees are crossed. If a grower crosses two such trees, the outcome is random and a probability model is given by outcomes:

I choose a card at random from a well-shuffled deck of 52 cards. There is a 1/4 probability that the card chosen is a spade, a 1/4 probability that the card is a heart, a 1/4 probability that the card is a diamond, and a 1/4 probability that the card is a club. Both spades and clubs are black cards, whereas hearts and diamonds are red. The events card is a heart and card is a club are:

The density curve for a continuous random variable X has which of the following properties?

A basketball player makes 70% of her free throws. When fouled, she gets to take two free throws. Let X represent the number of free throws made in two tries. The probability distribution for the number of free throws she makes in two attempts is summarized in the following table. _{The probability that she makes at least one free throw is expressed as:}

Assume that you are about to buy a car. There is a probability of 0.4 that you will purchase a new vehicle, and a probability of 0.5 that you will purchase a used vehicle. There is no probability that you will go home with more than one vehicle. Which of the following is true?

According to the M&Ms Web site, each package of the milk chocolate candies typically contains 14% brown, 13% red, 14% yellow, 16% green, 24% blue, and 20% orange M&Ms. You go to the store and buy a standard package. When you open it, you find that it contains 51 M&Ms, distributed as follows. Choosing one M&M from your bag is an example of:

You have lived in Columbus for more than 20 years and know that there is at least a 75% chance of a high temperature above freezing on a particular January day. This is an example of:

According to the M&Ms Web site, each package of the milk chocolate candies typically contains 14% brown, 13% red, 14% yellow, 16% green, 24% blue, and 20% orange M&Ms. You go to the store and buy a standard package. When you open it, you find that it contains 51 M&Ms, distributed as follows. Over the long run, you know that the probability of selecting a blue or an orange M&M will be 44%, because these outcomes are:

A geneticist is conducting research on pest-resistant walnut trees. He has developed a set of trees, when crossed, to produce offspring as follows: 50% of all trees are very resistant, 30% of trees are somewhat resistant, and 20% are susceptible to invasion by pest. The sample space consists of which of the following outcomes?

A geneticist developed a new type of pest-resistant walnut tree. These walnut trees produce 75% of pest-resistant walnut trees and 25% of susceptible (not resistant) trees when two resistant trees are crossed. If a grower crossed 100 such pairs of trees for 100 offspring, she will get:

The management for a chain of restaurants recorded the number of appetizers, X, ordered by tables dining. They observed that X had the following probability distribution. What is P(X < 2)?

An urn contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and count the number of red marbles in the 4 picks, the probabilities associated with this experiment are P(0) = 0.24, P(1) = 0.41, P(2) = 0.265, P(3) = 0.076, and P(4) = 0.009. The probability of at least 1 red marble is:

According to the Current Population Survey, the following table summarizes probabilities for randomly selecting a full-time student in various age groups: If we randomly select a full-time student, the probability that the student is not 18-24 years old is:

The high temperature X (in degrees Fahrenheit) on January days in Columbus, Ohio, varies according to the Normal distribution with mean 21 and standard deviation 10. If a January day in Columbus is randomly selected, what is the probability that the high temperature is between 15 and 25 degrees?

A geneticist developed a new type of pest-resistant walnuts. These walnuts produce 75% of pest-resistant walnut trees and 25% of susceptible (not resistant) trees when two resistant trees are crossed. If a grower crosses two such trees, the outcome is random and a probability model is given by:

To say that a coin is fair means that when it is tossed, each of the outcomes (heads or tails) has a 50% probability of occurring. This means that:

I roll a four-sided die. The possible outcomes are 1, 2, 3, or 4, depending on the number of spots on the side of the die that is face down. This collection of all possible outcomes is called:

I flip a coin twice and count the number of heads. Which of the following is a valid assignment of probabilities for the number of heads observed in two flips?