PROBABILITY TOPIC TEST MU ALPHA THETA 2007

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1 PROBABILITY TOPI TEST MU ALPHA THETA 00. Richard has red marbles and white marbles. Richard s friends, Vann and Penelo, each select marbles from the bag. What is the probability that Vann selects red marble and white marbles and Penelo selects red marbles and white marble? a 6 b c d. How many ways can six people sit around a circular table while leaving two empty seats? a 60 b 0 c 60 d 0. Joe is making a necklace for his girlfriend using an assortment of beads and a piece of string. How many ways can Joe arrange one red, one gold, one white, two blue, and three silver beads on the string? 0 b 0 c 60 d 60. Three fair six-sided dice are rolled. What is the probability that the number five appears on at least one of the dice? a 6 b 6 c 6 d 6. Fast fact : hris birthday is in September. Fast fact : The month of September has 0 days. What is the probability that out of a room of four people, all of whom have birthdays in September, two people are within a day of hris birthday? a b c d 6. The probability of event A occurring given that event B occurs is. The probability of event B occurring given that event A occurs is. There is a 6 probability that neither event A nor event B occurs. What is the probability of event A occurring? 0 a b c d not enough information

2 . What is the probability of rolling two fair six-sided dice and obtaining a sum that is a multiple of, given you rolled an even sum? b c d. On Thursday you present your one true love with a white rose. Each day, the rose has a probability to wilt of. Your true love will only accept your feelings if the rose survives for at least one week. What is the probability that your feelings are accepted and the rose wilts on a Saturday? a b c d 0 6. In order, Roger, Tiger, and Albert take turns rolling a fair, six-sided die. Whoever first rolls a three is crowned the MVP in all of sports (yes, it is a selective sample. What is the probability that Albert wins the MVP award? b 6 c d 0. If two events A and B are independent events, and the P(A =. and the P(B =., what is the P(A B? a. b. c.6 d.. Ethan has two urns, A and B. Urn A has three red marbles and six white marbles. Urn B has four red marbles and two white marbles. Ethan selects a marble from urn A and places it into urn B. He then proceeds to draw a marble from urn B. Given that Ethan draws a red marble from urn B, what is the probability that he had drawn a white marble from urn A? a b c d. What is the probability of selecting a prime number when you select a positive natural number less than? b c d. A particular cube has four faces colored yellow and two faces colored green. What is the probability that the two green faces are adjacent? a 6 b c d

3 . Robert encounters three kids, each with a probability of telling a lie. When Robert asks them whether they took his car keys the day before, two of the kids said yes and one said no. Assume that the probability of the kids taking the keys or leaving them is 0%, given you have no other information. What is the probability that the kids do indeed have Robert s car keys? 0 a 60 b c d. For any event E, let E be its complement. If P ( A B = and P ( A = P( A B P( B, what is the value of P ( A' B? Assume P ( A' B' = 0. a b c 0 d not enough information 6. A group of three duck hunters are all perfect shots. When three ducks suddenly fly over them, each duck hunter picks a random duck to shoot at. Assuming that all three duck hunters fired at the same time, what is the expected number of ducks that escaped? a 0 a 0 b c. Ten distinct points lie on a circle, how many distinct triangles can be formed using these points? a 0 b 0 c 0 d 60. Jonathan rolls a three sided die (with the numbers e, π, eight times. What is the probability that Jonathan rolls the same number at least five times in a row? 6 b c d. Let A be the number of ways three students out of a class of seven may sit in a row of three seats. Let B be the number of ways two students out of a class of seven may be selected to sit in a row of seats. Let be the number of ways three students may sit in a row of five seats. What is the value of A + B +? b c c 6 0. Which one of the following is equivalent to ( B ' ( A'? a B ( ' A b ( B' A c A ' d ( B' '

4 . indy s female budgey, Ruby, has a probability of suffering a nervous attack every time a stranger walks past her cage. Given that of the people who walk past Ruby s cage are strangers, what is the probability that Ruby will suffer a nervous attack when someone who is not a stranger walks past her cage? 0 b c d. In the game of poker, a full house is given by five-card hand containing a triple of one number and a double of another for example, three s and two kings. What is the probability of being dealt a full house? a d ( (!! b ( P c!(. In a standard deck of cards, let cards that are hearts or spades be considered to be cards of the mirror suit. What is the probability of drawing a mirror suited card, a black card, or an ace? b 6 0 c d. What is the probability that you flip at least heads in a row in trials using a fair coin? b c d 6. An urn contains the same number of blue and yellow marbles. marbles are drawn without replacement and the probability that they are the same color is. How many marbles were in the urn initially? b c d 6 6. Mr. Smith has children with at least girls. What is the probability that the youngest child is a girl? a b c d 6

5 . In how many ways may distinguishable crayons be placed into distinguishable boxes if no box may be left empty? 0 b 60 c 0 d 0. What is the probability of drawing two cards from a standard deck of cards and having one be a red card and one be a spade? 6 b c d. Five distinguishable one-sided keys (a one-sided key has one edge that is "flat" and one edge that is "bumpy" are placed on a key ring. In how many distinguishable ways may this be done? a 0 b 0 c 6 d 0. A deck of n cards consists only of red and green cards. When two cards are selected simultaneously and without replacement, the probability that they are both green is twice the probability that they are both red. What is the smallest possible value of n? a b c d 0. Steve has quarters, nickels, and penny. If Steve selects coins at random, what is the probability that the total value is exactly cents? a b c d 6 6. Evan and Alyssa, along with four other students, are seated in a row. What is the probability that Evan and Alyssa sit next to each other? a b c d. hris, Jason and Alex enter a fishing competition. Out of people who entered the tournament (hris, Jason and Alex are included, what is the probability that hris finishes in the top while Jason and Alex do not? 6 a b c d 6

6 . An unfair coin has a probability landing heads of. What is the probability of flipping the coin times and getting exactly heads? a b c d. An apartment building has units with separate mailboxes. One letter is sent to each unit, but the mailman is in a hurry and thus places one letter in each box at random. What is the probability that none of the letters are in the correct box? a b c d 6. If a chord is selected at random on a fixed circle, what is the probability that its length exceeds the radius of the circle? a b c d. Duels in the town of Discretion are rarely fatal. On the appointed day, each contestant comes at a random moment between A.M. and :0 A.M. and leaves exactly minutes later, honor served. However, if his opponent arrives within the time interval as well, the two will then fight. What fraction of duels leads to violence? a 6 b 6 c d. You shuffle an ordinary deck of playing cards containing four aces. You then turn up cards from the top of the deck until the first ace appears. On the average, how many cards do you turn before you produce the first ace? a. b 0. c 0.6 d.0. Inscribed on a table of infinite expanse is a set of parallel line spaced 6 units apart. A needle of length is twirled and tossed on the table. What is the probability that when it comes to rest it crosses a line? a π b c d π 0. What is the probability that you flip a head or tail when you flip a fair coin? a b c d

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