10 probability questions
. This assignment has 11 questions, for a total of 18 points . The only one way to submit your homework is the dropbox. . Late assignments will be severely penalized. This penalty is currently a 1% deduction every six minutes or part thereof until the end of the tenth hour after the deadline, after which submissions will receive no credit. Name: 1 (2 points) Determine whether the following statements are True or False: (a) _ Probability is a number between 0 and 1. (b ) As the number of trials increase, the experimental probability gets closer to the- oretical probability. (c) If an event is impossible to occur, its probability is undefined. (d) In combination, order of selection does matter. (2 points) In a given week, a veterinarian treated the following animals. Determine the followings (express your answers as a simplified fraction): Animal Number Treated Dog 50 Cat 35 Bird 12 Rabbit 8 (a) Probability that the next animal she treats is a dog (a) . (b) Probability that the next animal she treats is a cat (b) (c) Probability that the next animal she treats is a rabbit (c) (d) Probability that the next animal she treats is a dog or a bird (d) 3 (2 points) You are dealt one card from a standard 52-card deck. Find each of the following probabilities. Express your answers a simplified fraction: (a) probability of being dealt a queen (a)MGF 1106 Homework 7 Page 2 of 4 (b) probability of being dealt a club (c) probability of being dealt the king of spades (b) (d) probability of being dealt a card with green heart (c) (d) 4 (2 points) a fair die is rolled. Find each probability. Express your answers a simplified fraction: (a) probability of rolling a 6 (a) (b) probability of rolling a number less than 1 (b) (c) probability of rolling a number between 1 and 4, exclusive. (c) (d) probability of rolling a number less than 5 (d) 5 (1 point) Suppose there's a game where the player rolls a die, and either wins or loses money according to these rules. die roll 1 2 3 4 5 6 outcome | lose $2 |lose $2 |lose $2 |win $1 |win $1 win $10 Calculate the expected value. 5 6 (1 point) One way to bet in roulette is to place $1 on a single number. Recall that game has 38 numbered slots (1 through 36, 0 and 00). If the ball lands on that number you are awarded $35 and get to keep the $1 that you paid to play the game. If the ball lands on any other 37 slots, you are awarded nothing and the $1 that you bet is collected. Find the expected value for playing roulette if you bet $1 on number 20. Round your answer to 4 decimal places. 6 7 (1 point) Five hundred raffle tickets are sold for $4 each. One prize of $500 is to be awarded. Raul purchases one ticket. (a) Determine his expected value. (a)MGF 1106 Homework 7 Page 3 of 4 (b) Determine the fair price of a ticket. (b ) 8 (1 point) Assume that the spinner cannot land on a line. Determine the following odds: (a) the odds against the spinner landing on the color red. (a) (b) the odds in favor the spinner landing on the color green or red. (b) 9 (2 points) Of the 38 plays attributed to Shakespeare, 18 are comedies, 10 are tragedies, and 10 are histories. one play is randomly selected from Shakespeare's 38 plays. (a) Find odds in favor of selecting a comedy. (a) (b) Find odds against selecting a history. (b) (c) Find odds in favor of selecting a tragedy or a history. (c) (d) Find odds against selecting a comedy or a history. (d) 10 (2 points) A hat contains four marbles: 1 yellow, 1 red, 1 blue, and 1 green. Two marbles are to be selected at random without replacement from the hat. Express your answers a simplified fraction: (a) Construct a tree diagram and list the sample space.MGF 1106 Homework 7 Page 4 of 4 (b) Determine the probability of selecting exactly 1 red marble. (b) (c) Determine the probability of selecting at least 1 marble that is not red. (c) (d) Determine the probability of selecting no green marbles. (d) 11 (2 points) You decide to take a science course, an English course, and a mathematics course during the next term. The available courses that you can take are listed below. Express your answers a simplified fraction: Science English Mathematics Biology Composition Algebra Geology Literature Statistics Physics Calculus Oceanography If the courses are selected at random, (a) Construct a tree diagram and list the sample space. (b) Determine the probability that Calculus is selected. (b) (c) Determine the probability that geology and literature are selected. (c) (d) Determine the probability that oceanography is not selected. (d)
