Name: Class: Date: Probability/Counting Multiple Choice Pre-Test

Transcription

1 Name: _ lass: _ ate: Probability/ounting Multiple hoice Pre-Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1 The dartboard has 8 sections of equal area. The letters represent the colors red (R), yellow (Y), blue (), and green (G). Use a table to show the probability distribution for a dart that hits the board at a random location. olor R Y G Probability olor R Y G Probability olor R Y G Probability olor R Y G Probability t the Rockville Middle School carnival, 12 of the first 120 people who played the ring toss game won the first prize, 24 won the second prize, and 36 won the third prize. What is the experimental probability of winning the first, second, or third prize? 60% 50% 45% 40%

2 3 How many different 3-letter arrangements can be made from the word T? If a student tosses a fair coin four times. Each time she got a tails. What is the probability her next toss will be a heads? couple has three children, what is the probability that they are boy, girl, boy, in that order? student is using a 6-sided die. He also tosses a fair coin. What is the correct sample space for this compound event? {H, T} {(1,H), (2,H), (3,H), (4,H), (5, H), (6, H),(1,T), (2,T), (3,T), (4,T), (5,T), (6, T)} {(HT, 1), (HT, 2), (HT, 3), (HT, 4), (HT, 5), (HT, 6)} {1, 2, 3, 4, 5, 6} 7 film festival has 8 interns available during the summer. How many different ways can the Festival irector hire six of the eight interns? oes this situation represent a combination or a permutation? 6, combination 20,160; permutation 8, permutation 28, combination lgebra II Probability/ounting Pre-Test Page 2

3 8 The table shows the results of a survey of students in two math classes. Find P(more than 1 hour of TV 3rd period class). Round to the nearest thousandth. id You Watch More Than One Hour of TV Last Night? Yes No 3rd period class th period class Suppose a fair coin is tossed and a 6-sided number cube is rolled. What are the chances that the coin lands on tails and the outcome on the number cube is a number greater than 3? The students in an English class are creating nonsense 6-letter words. What is the probability that a word will end in Q? 1 11,881, Mr. Gle brought a cooler containing drinks to his daughter s soccer game. There are 10 sports drinks, 5 cans of orange juice, and 3 sodas. If a drink is selected at random from the cooler, what is the probability that it is a sports drink? lgebra II Probability/ounting Pre-Test Page 3

4 12 coin is tossed and a die is rolled. What is the probability that the coin shows tails and the die shows a two? Every morning Mrs. Post walks from her house to each of the farm s other structures. There are 3 barns, a workshop, a chicken coop, and the house on the property. She varies the order in which she walks to each structure to shorten or lengthen her walking distance. In how many different orders can Mrs. Post, beginning at her house, walk to each of the farm s other structures and then return to her house? If no digit appears more than once, how many 3-digit numbers can be formed from the digits 2, 3, 4, 5, 6, 7, 9? You and 4 friends play a game where each person writes down his or her name on a scrap of paper, and the names are randomly distributed back to each person. Find the probability that everyone gets back his or her own name lgebra II Probability/ounting Pre-Test Page 4

5 16 club of students wants to select their officers by random drawing. There are 7 seniors, 7 juniors, and 6 sophomores in the club. Three names will be drawn. The first person chosen will be the president, the second will be the treasurer, and the third will be the secretary. Which expression can be used to calculate the probability that all the officers will be juniors? 17 Which expression is equivalent to 18 Use Pascal s Triangle to find the binomial coefficients:. 66; ; ; ; coin is tossed 11 times. What is the probability of obtaining exactly 9 heads? lgebra II Probability/ounting Pre-Test Page 5

6 20 Use the tree diagram below to create the sample space from flipping 3 coins. Then determine the probability of flipping exactly 2 heads. HHH, HHT, HTH, HTT, THH, THT, HHH, HHT, HTH, HTT, THH, THT, TTH, TTT; P(2H1T) = 1 8 TTH, TTT; P(2H1T) = 1 3 HHH, HHT, HTH, HTT, THH, THT, HHH, HHT, HTH, HTT, THH, THT, TTH, TTT; P(2H1T) = 8 3 TTH, TTT; P(2H1T) = Suppose you are choosing a 3-digit personal access number using digits from 1 through 3 where no digit can be repeated. What is the sample space of all possible access numbers? 111, 112, 113, 123, 121, 122, 131, 132, 133, 211, 212, 213, 221, 222, 223, 311, 312, 312, 321, 322, 323, 331, 332, , 222, 333, 123, 132, 213, 231, 321, , 132, 213, 231, 321, , 321, 213, 231 Suppose S and T are independent events. Find P(S and T). 22 P(S) = 0.32, P(T) = lgebra II Probability/ounting Pre-Test Page 6

7 23 P(S) = 3 5, P(T) = Suppose Q and R are mutually exclusive. Find P(Q or R). 24 P(Q) = 17%, P(R) = 42% 7.14% 25% 59% 714% 25 P(Q) = 1 2, P(R) = lgebra II Probability/ounting Pre-Test Page 7

8 26 onsider and are independent events, and P() = 0.25 and P() = Fill in the missing probabilities on the Venn iagram below. P( ) = 0.08, P()=0.25, P() = 0.32, P()= 0.35 P( ) = 0.08, P()=0.17, P() = 0.24, P()= 0.35 P( ) = 0.08, P()=0.25, P() = 0.32, P()= 0.51 P( ) = 0.08, P()=0.17, P() = 0.24, P()= If all possible results are equally likely and mutually exclusive, what is the probability that a spin of the spinner will land on an upper case letter that is also a vowel? lgebra II Probability/ounting Pre-Test Page 8

9 28 Two urns contain white balls and yellow balls. The first urn contains 8 white balls and 8 yellow balls and the second urn contains 4 white balls and 3 yellow balls. ball is drawn at random from each urn. What is the probability that both balls are yellow? Use the Venn diagram below to determine the probability of a digit between 1-10 being both odd and prime couple would like to have two children, what is the probability that they will be the same sex? lgebra II Probability/ounting Pre-Test Page 9