Exam 4: Probability: the Study of Randomness

Suppose Team A has a 0.75 probability to win their next game and Team B has a 0.85 probability to win their next game.Assume these events are independent.What is the probability that Team A wins exactly two of their next three games?

Suppose you have two math classes (math 1 and math 2)and two sciences courses (science 1 and science 2)that you must complete before your sophomore year in college.Assume your college is on a semester system and there are two semesters in each year.What is the sample space for the number of required math classes you take during your freshman year?

A standard deck of cards has 52 cards.The cards have one of two colors: 26 cards in the deck are red and 26 are black.The cards have one of four denominations: 13 cards are hearts (red),13 cards are diamonds (red),13 cards are clubs (black),and 13 cards are spades (black).Two cards are selected at random and the color is recorded.Which of the following is the correct sample space S for the set of possible outcomes?

A standard deck of cards has 52 cards.The cards have one of two colors: 26 cards in the deck are red and 26 are black.The cards have one of four denominations: 13 cards are hearts (red),13 cards are diamonds (red),13 cards are clubs (black),and 13 cards are spades (black).Two cards are selected at random.Event C is defined as the event that the first card is clubs,event R as the event that the first card is red,and event B as the event that the second card is black.Which events are disjoint?

Normal distributions represent _______ random variables.

If you draw an M&M candy at random from a bag of the candies,the candy you draw will have one of six colors.The probability of drawing each color depends on the proportion of each color among all candies made.Assume the table below gives the probabilities for the color of a randomly chosen M&M. If you select two M&M's and the colors are independent,then what is the probability that both are the same color?

The probability distribution of random variable X is defined as follows. Is the above a valid probability model?

The amount of time it takes you to complete an exam in a statistics course is an example of a _______ random variable.

A probability histogram describes the probability distribution of a discrete random variable.

A standard deck of cards has 52 cards.The cards have one of two colors: 26 cards in the deck are red and 26 are black.The cards have one of four denominations: 13 cards are hearts (red),13 cards are diamonds (red),13 cards are clubs (black),and 13 cards are spades (black).Two cards are selected at random and the denomination is recorded.The event D is defined as the event that the first card is diamonds and the second card is red.Which of the following correctly defines event D^C?

Suppose Team A has a 0.75 probability to win their next game and Team B has a 0.85 probability to win their next game.Assume these events are independent.What is the probability that both Team A and Team B win?

Football is a very popular sport in the United States.The National Football League (NFL)is composed of 32 teams.Every year there is a football draft where players are selected for each of the teams.Football players in the United States can make millions of dollars and must be very good at the sport to make a team.Would being selected for an NFL team be considered a random phenomenon?

The statistics of a particular basketball player state that he makes 4 out of 5 free-throw attempts.The basketball player is just about to attempt a free throw.What do you estimate the probability that the player makes this next free throw to be?

A valid probability is either 0 or 1.

Ignoring twins and other multiple births,assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5.Define events A = {the next two babies are boys} and B = {at least one of the next two babies is a boy}.What do we know about events A and B?

The United States has 10 federal holidays.Each holiday and the date of the holiday in 2016 are listed in the table below. You work in Washington,DC,and you are looking forward to enjoying the day off on the federal holidays.There are high chances of snow in Washington,DC,from November to March.What is the sample space for the federal holidays that could occur during a winter snow storm in Washington,DC?

At the end of a production run manufacturing rubber gaskets,items are sampled at random and inspected to determine if the item is acceptable (A)or defective (D).Suppose it is planned to select two items and determine if each is either A or D.What is the sample space S of the outcomes?

What is the sample space for the number of text messages the average teenager sends per month?

Thirty random students are selected and asked questions about their favorite type of car.All the colors of their favorite car are an example of a discrete random variable.

Is the probability Z > 1 the same as the probability that Z  1? (The figure below is a standard Normal probability distribution. )