4. Probability

In computing classical probabilities, all outcomes must be equally likely. Explain what this means.

Define each of the following.

c. Event

Define each of the following.

d. Sample space

Define each of the following.

e. Equally likely outcomes

Define each of the following.

f. Impossible event

Define each of the following.

g. Unusual event

[NW] Verify that the following is a probability model. What do we call the outcome “blue”?

Why is the following not a probability model?

A student is taking a 40-question multiple-choice exam. Each question has five possible answers. Because the student did not study, he guesses on every question. Using 0 or 1 to represent a correct answer, use the following line of random digits to simulate the probability that the student will guess a question correctly.

73634 79304 78871 25956 59109 30573 18513 61760

[NW] Made in America In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, “When you see an ad emphasizing that a product is ‘Made in America,’ are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?” The results of the survey, by age group, are presented in the following contingency table.

c. Are 18- to 34-year-olds more likely to buy a product emphasized as ""Made in America"" than individuals in general?

The following represent the results of a survey in which individuals were asked to disclose what they perceive to be the ideal number of children.

d. Among the females, what is the probability the individual believes the ideal number of children is 2?

You are planning a trip to a water park tomorrow and the weather forecaster says there is a 70% chance of rain. Explain what this result means.

Text Twist

In the game Text Twist, six letters are given and the player must form words of different lengths using those letters. Suppose the letters in a particular game are ENHSIC.

c. The solution to this game has three 6-letter words. To move to the next round, the player must get at least one of the six-letter words. If the player simply guesses, what is the probability of getting one of the six-letter words on the first try?

Lingo

In the gameshow Lingo, the team that correctly guesses a mystery word gets a chance to pull two Lingo balls from a bin. Balls in the bin are labeled with numbers that match the numbers still on the team's Lingo board. There are also three prize balls and three red "stopper" balls in the bin. If a stopper ball is drawn first, the team loses its second draw. To form a Lingo, the team needs five numbers in a row—vertically, horizontally, or diagonally. Consider the sample Lingo board below for a team that has just guessed a mystery word.

a. What is the probability that the first ball selected is on the Lingo board?

Roulette

In the game of roulette, the wheel has 38 slots numbered 0, 00, 1, 2, …, 36. A metal ball is spun around the wheel and can land in any of the slots. The slots numbered 0 and 00 are green, the odd numbers are red, and the even numbers are black..

d. Determine the probability that the metal ball lands in both the number 31 slot and a black slot at the same time. What term is used to describe this event?