3.2 Classical probability practice 4

You and a friend are playing Yahtzee. Yahtzee is a game where players roll 5 dice an try to collect sets of numbers. On each turn, player is given 3 rolls of the dice. The first roll is of is of all 5 dice together. The player then selects 0-5 dice to “re-roll”. She re-rolls these dice. The player again selects 0-5 dice to re-roll a seconds times. She re-rolls these dice then, selects how to score the dice. Answer the following questions in fraction. Note that [math]6^4=1296[/math]

(a) Yahtzee is 5 of the same number. What is the probability that you roll the dice and get a Yahtzee?

(b) A four-of -a-kind is four matching dice and one die that does not match. What is the probability of getting a four-of-a-kind on the first roll?

On your first roll you get: . You decide to go for a Yahtzee, a four-of a kind, or a full house (three of a kind and two of a kind). So you keep the and roll the again.
(c) On your second roll,what is the probability that you roll these two dice and get two 2s, or a 2 and some other number, or two of kind of some other number?

(d) Starting with ,what is the probability that you get Yhatzee in the next two rolls? That is ,find the probability of turning theinto within two rolls.

Box A contains a red marble, a blue marble, and a yellow marble. Box B contains a red marble, a blue marble, a yellow marble and a green marble. One marble is taken from each box. What is the probability that both marbles are the same colour?

200 people with neurology symptoms, which include headaches and backaches, participated in a study to evaluate a pain relief medicine. All the people took the medicine and the results were as follows:

• 60 people experienced headache relief
• 126 people experienced backache relief
• 6 people experienced relief from both

What is the probability that a person who takes the drug experiences relief from (use fractions to express your answers)

(a) At least one of the two symptoms?

(b) Neither of the symptoms?

A bag contains balls numbered 1 through 30. Two balls are chosen at random with replacement. What is the probability that: (use fractions to express your answers)

(a) both numbers are odd?

(b) one number is even and the other is odd?

(c) both numbers are less than 10.

(d) the same number is chosen twice?

Two six-sided dice are rolled. Find the probability that the sum is greater than 7 or the sum is even.

In an exam, two independent reasoning problems, 1 and 2, are asked. 35% students solved problem 1 and 15% students solved both the problems. What percentage of students who solved the first problem will also solve the second one?

In a high school graduating class of 128 students, 52 are on the honor roll. Of these, 48 area going on to college; and of the other 76 students, 56 are going to college. If a student is selected at random from the class, what is the probability that the person chosen is: (use fractions to express your answers)

(a) going to college?

(b) not going to college?

(c) not going to college and on the honor roll?

(Calculator) A shipment of 25 television sets contains three defective units. What is the probability that a vending company purchasing four of these units and receive

(a) All good units?

(b) Two good units?

(c) At least two good units?

(Calculator) Three prizes are rewarded in a raffle during a halftime show at a school basketball game. Ben, James, Ashley, and [math]17[/math] other students each have one ticket. Use fractions to express your answers

(a) If the raffle has a first, second, and third prize, what is the probability, as an exact value, that Ben wins first prize, James wins second prize, and Ashley wins third prize?

(b) If the raffle has three identical prizes, what is the probability that Ben, James, and Ashley win the prizes?

Chess is a game played by two players. A game results in one of three mutually exclusive outcomes-either player A wins, or player B wins, or the game results in a draw. In a world championship chess match, the Russian champion Kozlov and the American champion Armstrong are involved in a sudden death payoff. The first player to win a match wins the championship. From previous results, the probability that Kozlov wins a match is [math]\dfrac{1}{3}[/math] and the probability that Armstrong wins a match is [math]\dfrac{1}{4}[/math]. Calculate the probabilities that: (use fractions to express your answers)

(a) the first match is a draw.

(b) the championship has not been decided after the second match.

(c) Armstrong wins within two matches.

(Calculator) From [math]6[/math] biologists, [math]4[/math] chemists, and [math]3[/math] physicists, a scientific committee of [math]5[/math] is to be chosen. The top two scientists-April, a biologist, and Lee Kim, a chemist must be on the committee.

(a) What is the probability that at least [math]3[/math] biologists are chosen?

(b) What is the probability that at least [math]1[/math] physicist is chosen?

(c) What is the probability that the [math]3[/math] remaining members chosen are all from the same branch of science?

A golfer is practicing putting. The probability that he holes the first putt is [math]0.4[/math]. Each time he holes a putt the probability that he holes the next putt increases by [math]25\%[/math]. Each time he misses a putt the probability that he misses the next putt increases by [math]20\%[/math]. Calculate the probability that: (use fractions to express your answers)

(a) he holes the first two putts

(b) he misses the first two putts

(c) he holes two of the first three putts