Exam 10: Probability and Counting Techniques

In one lottery game, contestants pick six numbers from 1 through 40 and have to match all six for The big prize (in any order). What's the probability you'll win if you buy one ticket?

A coin is tossed and then a die is rolled. Find the probability of getting a 5 on the die given that the Coin landed tails up.

In any experiment, the set of all possible outcomes is called the .

Four balls are numbered 1 through 4 and placed in a box. Two balls are selected without replacement. Find the probability that (a)the sum of the numbers is even. (b)the number on the second ball is less than the number on the first ball. (c)the sum of the numbers on both balls is greater than 3.

In a shop there are 25 customers, 20 of whom will make a purchase. If three customers are selected, One at a time, at random, what is the probability that all will make a purchase?

Two dice are rolled. Find the probability that the sum was a 7 given that one of the numbers was a 5.

Suppose this diagram illustrates the number of women and Democrats in the U.S. Senate. The probability that a senator is either female of Democrat can be calculated as . Describe what the three fractions at the end of this calculation represent in terms of probability.

Draw a tree diagram to determine the sample space when three coins are tossed.

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a 4 of Diamonds.

If two people are selected at random, what is the probability that they were both born in May?

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a diamond or A 10.

Two dice are rolled. Find the probability of getting a 5 on one die or on both dice.

In a certain geographic area, 40% of the inhabitants are pet owners. If four inhabitants are selected at random, what is the probability that all will be pet owners?

Find the probability using the binary probability formula. Round to four decimal places, if necessary.

When an event can't possibly occur, its probability is . When an event is certain to occur, its probability is .

Find both the number of combinations and the number of permutations for the given number Of objects. 10 objects taken 7 at a time

A person rolls two dice and wins if the sum is 7. What are the odds in favor of winning? What are the odds against winning?

Decide whether the following is a binomial experiment. Drawing a card from a deck and seeing what suit it is

Evaluate the expression. (4!)(3!)

In December 2008, 500 men and 500 women were surveyed by Omnitel about their opinion on whether federal government bailout money should be used to help homeowners in default. The number giving each response is shown below. a. If a person who participated in the survey is selected at random, what is the probability that he or she answered no? b. What is the probability that the person selected is a man who answered either yes or no? c. Based on the data from the survey, if you had stopped a random woman on the street in December 2008 and asked her opinion, what is the probability that she would have said that bailout money should not be used to help homeowners in default? d. Which type of probability (empirical or theoretical)are you using to answer these questions? Explain.