Objective: The student will be able to determine sample spaces From the information provided, create the sample space of possible outcomes. 1) Flip a coin twice. Solution: S = {HH, HT, TH, TT} 3) Both Fred and Ed have a bag of candy containing a lemon drop, a cherry drop, and a lollipop. Each takes out a piece and eats it. What are the possible pairs of candies eaten? Solution: S = { lemon lemon, lemon cherry, lemon lollipop, cherry lemon, cherry cherry , cherry lollipop, lollipop lemon , lollipop cherry , lollipop lollipop} 4) Two white mice mate. The male has both a white and a black fur-color gene. The female has only white fur-color genes. The fur color of the offspring depends on the pairs of fur-color genes that they receive. Assume that neither the white nor the black gene dominates. List the possible outcomes. Solution: S = {WW,BW} Objective: The student will be able to ﬁnd the probability of an event, using classical probability or empirical probability. Find the indicated probability. 5) A sample space consists of 174 separate events that are equally likely. What is the probability of each? Solution: P = 1/174 6) On a multiple choice test, each question has 5 possible answers. If you make a random guess on the first question, what is the probability that you are correct? Solution: P = 1/5 7) A die with 6 sides is rolled. What is the probability of rolling a number less than 5? Solution: P = 4/6 = 2/3 8) A bag contains 2 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? Solution: P = 3/12 = 1/4 9) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 4? Solution: P = 3/36 = 1/12 10) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years. Solution: P = 31/365 = 0.849 11) A class consists of 66 women and 98 men. If a student is randomly selected, what is the probability that the student is a woman? Solution: P = 66/164 = 0.402 12) The data set represents the income levels of the members of a country club. Find the probability that a randomly selected member earns at least $97,000. Round your answers to the nearest tenth. 101,000 105,000 87,000 107,000 92,000 101,000 97,000 77,000 111,000 121,000 82,000 99,000 109,000 92,000 105,000 103,000 97,000 113,000 72,000 103,000 Solution: P = 14/20 = 7/10 = 0.7 13) Refer to the table which summarizes the results of testing for a certain disease. If one of the results is randomly selected, what is the probability that it is a false positive (test indicates the person has the disease when in fact they don't)? What does this probability suggest about the accuracy of the test? Solution: P = 26/273 = 0.095 , it must be very small value for the accuracy of the test 14) Refer to the table which summarizes the results of testing for a certain disease. If one of the results is randomly selected, what is the probability that it is a false negative (test indicates the person does not have the disease when in fact they do)? What does this probability suggest about the accuracy of the test? Solution: P = 4/309 = 0.0129 , it must be very small value for the accuracy of the test. Estimate the probability of the event. 15) A polling firm, hired to estimate the likelihood of the passage of an upcoming referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is: 1 = FOR, 2 = AGAINST. If the referendum were held today, estimate the probability that it would pass. 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1 Solution: P = 12/20 = 3/5 = 0.6 16) Of 1982 people who came into a blood bank to give blood, 340 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure. Solution: P = 340/1982 = 0.171 Find the indicated complement. 17) If P(A) = 1/7 , find ̅̅̅̅ Solution: ̅̅̅̅= 1 – = 18) Find ̅̅̅̅, given that P(A) = 0.732. Solution: ̅̅̅̅= 1 – 0.732 = 0.268 19) Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.185. Find the probability that in a given year it will not snow on January 1st in that town. Solution: ̅̅̅̅ = 1 – 0.185 = 0.815 20) The probability that Luis will pass his statistics test is 0.90. Find the probability that he will fail his statistics test. Solution: ̅̅̅̅ = 1 – 0.90 = 0.10 21) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. Solution: ̅̅̅̅ 1 = = 0.915 Find the indicated probability. 22) A spinner has equal regions numbered 1 through 21. What is the probability that the spinner will stop on an even number or a multiple of 3? Solution: P(A = P(A) + P(B) – P(A = + - = = 23) If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade? Solution: : P(A = P(A) + P(B) – P(A = + - = = 24-He should be able to find the probability of compound events , using the addition rules when two events are mutually exclusive. 25- He should be able to find the probability of compound events , using the addition rules when two events are not mutually exclusive. 26- He should be able to find the probability of compound events , using the addition rules when two events are not mutually exclusive. ( ) 27- He should be able to find the probability of compound events , using the addition rules when two events are not mutually exclusive. ( ) ( ( ) ) 28- He should be able to find the probability of compound events , using the addition rules when two events are mutually exclusive. 29- He should be able to find the probability of compound events , using the addition rules when two events are mutually exclusive. 30- He should be able to find the probability of complementary events , using the rule. 31- He should be able to find the probability of two independent events , using the multiplication rules. 32- He should be able to find the probability of two independent events , using the multiplication rules. 33- He should be able to find the probability of two independent events , using the multiplication rules. 34- He should be able to find the probability of x successes in n trials of a binomial experiment. ( ) 35- He should be able to find the probability of two independent events , using the multiplication rules. 36- He should be able to find the probability of two independent events , using the multiplication rules. 37- He should be able to find the probability of two independent events , using the multiplication rules. 38- He should be able to find the probability of two independent events , using the multiplication rules. 39- He should be able to find the probability of x successes in n trials of a binomial experiment. ( )( ) ( ) ( ) 40- He should be able to find the probability of x successes in n trials of a binomial experiment. 41- He should be able to find the probability of x successes in n trials of a binomial experiment.

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