Exam 10: Probability and Counting Techniques

Three cable channels (95, 97, and 103)air quiz shows, comedies, and dramas. The numbers of Shows aired are shown here. If a show is selected at random, what is the probability that the show is on Channel 103 or it is a comedy?

How many different ways can a college select three applicants for a teaching position from a pool of 20 applicants?

In the game of rock, paper, scissors, two people play, and it's equally likely that you will win, lose, Or tie. Find the probability of losing at least once in two tries.

In a classroom, the students are 14 boys and 4 girls. If one student is selected at random, find the Probability that the student is a girl.

Find the probability of getting any triple-digit number where all the digits are the same in a lottery Game that consists of picking a three-digit number using the digits 1 to 8. Round to three decimal Places, if necessary.

Four red cards are numbered 1, 2, 3, and 4. Three black cards are numbered 5, 6, and 7. The cards are placed in a box and one card is selected at random. What is the probability that a red card was selected given that the number on the card was an even number?

Decide if the two events described are independent or dependent. Flipping a coin and then flipping it again

Every member of Congress declares a single party affiliation, either Democrat, Republican, or Independent. Assume that a random member of Congress is being chosen and decide whether or not The given events are mutually exclusive. The representative is from a state west of the Mississippi, the representative is a man.

In the game of rock, paper, scissors, two people play, and it's equally likely that you will win, lose, Or tie. Find the probability of losing twice in a row.

A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, what is the probability that it is green?

At a community college, there are 7 English instructors, 6 math instructors, and 6 history instructors. If one of these instructors is selected at random to serve on a committee, find the probability that the instructor is an English instructor or a history instructor.

A single card is drawn from an ordinary 52-card deck. Find the probability of getting a red 6.

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

In the game of rock, paper, scissors, two people play, and it's equally likely that you will win, lose, Or tie. Find the probability of having the same outcome twice in a row.

Two dice are rolled. Find the probability of getting a sum less than or equal to 4.

For an event E in a sample space, the set of all outcomes that are not in E is called the of E.

When two dice are tossed, find the odds against getting a sum of 8.

If the probability of event B is given by , then find the odds in favor of and against C.

Decide whether the selection described is a combination or a permutation. Three prizes are given to the winners of a race.

The odds in favor of an event are 1:7. Find the probability that the event will occur.