binomial and geometric

A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contains the tap water. Assuming that people cannot taste a difference between bottled water and tap water, what is the probability that at least 8 of the 9 participants will correctly identify the tap water?

• 0.0020

• 0.0195

• 0.8889

• 0.9805

• 0.9980

A carnival game allows the player a choice of simultaneously rolling two, four, six, eight, or ten fair dice. Each die has six faces numbered 1 through 6, respectively. After the player rolls the dice, the numbers that appear on the faces that land up are recorded. The player wins if the greatest number recorded is 1 or 2. How many dice should the player choose to roll to maximize the chance of winning?

• Two

• Four

• Six

• Eight

• Ten

A popular computer card game keeps track of the number of games played and the number of games won on that computer. The cards are shuffled before each game, so the outcome of the game is independent from one game to the next and is based on the skill of the player. LetXrepresent the number of games that have been won out of 100 games. Under which of the following situations wouldXbe a binomial random variable?

• All games were played by the same player, whose skill improved over the course of the 100 games

• A group of 5 players of different skill levels were each allowed to play 20 games in a row.

• A group of players of different skill levels were each allowed to play until they had lost 3 games and this resulted in 100 games played.

• Two players of equal skill level each played one game a day for 50 days and their skill level did not change from day to day.

• Two players of different skill levels competed by allowing one player to continue until a game was lost, then the other player to continue until a game was lost, and so on, until 100 games were played.

The probability of winning a certain game is 0.5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are n=10, n=20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?

• n=10 only

• n=20 only

• n= 100 only

• n=10 or n=20 only; the probabilities are the same.

• n=10 or n=20 or n=100 ; the probabilities are the same.

Circuit boards are assembled by selecting 4 computer chips at random from a large batch of chips. In this batch of chips, 90 percent of the chips are acceptable. LetXdenote the number of acceptable chips out of a sample of 4 chips from this batch. What is the least probable value ofX?

• 0

• 1

• 2

• 3

• 4

The probability of obtaining a head when a certain coin is flipped is about 0.65. Which of the following is closest to the probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times?

• 0.14

• 0.37

• 0.39

• 0.60

• 0.65