Probability Warm-Up 2 Directions Solve to the best of your ability. (1) Write out the sample space (all possible outcomes) for the following situation: A dice is rolled and then a color is chosen, blue or green. (2) How many different meals can you create from two proteins, four vegetables, and four breads? (3) How many unique passwords can you create when choosing four numbers between 0 and 9 if repeated values are not allowed? (4) If 16 students are to take a quiz, are four question enough to make sure that each student s quiz questions are in a different order? (5) The volleyball team will include 6 Juniors and 6 Seniors. How many teams can be created if 10 Junior and 14 Seniors try out? (6) Two dice are rolled, what are the odds that both dice will show even numbers?
Guiding Question: How likely is it that I will win the lottery? Hint; Not very! Relevant Vocabulary: Sample space, outcome, event, likelihood, probability, fraction, independence, dependence, complimentary probability, conditional probability Questions: In general, to calculate the probability of an event winning the lottery or any other you have to know or at least be able to estimate all possible outcomes and the number of desirable outcomes: Take the lottery for example Example 1 A simple lottery involves selecting a number between 0 and 1000. The winner gets 100 dollars. Each ticket costs a dollar. If you buy 20 tickets how likely are you to win the lottery? Of course most lotteries are much more complex. Example 2 In the Texas Lottery you pick six numbers between 1 and 54 inclusive. Each number may only be used once and the order of the numbers does not influence whether you win or lose. If you match all six numbers you win the jackpot. How likely are you to win the jackpot if you buy ten tickets? First ask yourself How many different ways can you select six numbers from a group of 54 without replacement or concerning yourself with order? Hint; is this a permutation or a combination? Then apply the formula. The complimentary probability is instructive here. Subtract your odds of winning from the number 1. The answer you get is the likelihood of losing the lottery. Summary:
Guiding Question: How does driving your car influence the odds that you are allergic to dairy? Hint; it doesn t. Questions: What is the difference between dependent and independent events? Drawing numbers for a lottery is a classic example of dependent events because the lottery numbers are removed from the game after they are drawn. That is, the odds of one of your numbers being picked are slightly higher after each number is called. Considering the previous example more closely: Suppose you are the lucky winner and all of your numbers are called. What were the odds of one of your numbers being drawn on the first pull? The second? The third? Ect Draw 1 Draw 2 Draw 3 Draw 4 Draw 5 Draw 6 Describe the pattern and the reasons for the pattern in the table. Let s consider a different kind of lottery that is based on independent events. In this lottery, the outcome of one event will not influence that of the next. Example 3 Six dice are rolled. You choose one number for each dice. If you guess all six dice values correctly you win the jackpot. What are the odds of guessing the correct numbers for each dice? Roll 1 Roll 2 Roll 3 Roll 4 Roll 5 Roll 6 Describe the pattern and the reasons for the pattern in the table. Summary:
Guided Practice 1 A die is rolled and a coin is flipped. Are these events independent? What is the likelihood that the dice roll is even and the coin flip is heads? Guided Practice 2 A bag of assorted candy contains 16 pieces, 4 of which are Jolly Ranchers. You draw two candies without replacement. Are the events independent? How likely is it that both candies are Jolly Ranchers? Guided Practice 3 A bag of assorted candy contains 16 pieces, 4 of which are Jolly Ranchers. You draw two candies with replacement. Are the events independent? How likely is it that both candies are Jolly Ranchers? Guided Practice 4 At the end of the 1930s, roughly 12% of American s owned a car. Also in the 1930s, roughly 2% of people were allergic to dairy. Are these independent events? What was the probability of someone with a dairy allergy owning a car in the 1930s? Summary:
M n2n0q1l8\ zkrugtxar VS]oafUtCwwairPeD HLZLMCj.] _ EAylPlL NrxiHggh_tHsF NrzeFsveKrRvce\db. Determine whether the events are independent or dependent. Then find the probability. 1) You roll a fair six-sided die twice. The first roll shows a one and the second roll shows a two. 2) A basket contains eight apples and four peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit. Both pieces of fruit are apples. 3) A bag contains eight red marbles and five blue marbles. You randomly pick a marble and then return it to the bag before picking another marble. Both the first and second marbles are red. 4) A bag contains eight red marbles and three blue marbles. Another bag contains seven green marbles and eight yellow marbles. You randomly pick one marble from each bag. One marble is blue and one marble is yellow. 5) A basket contains eight apples and eight peaches. You randomly select a piece of fruit and then return it to the basket. Then you randomly select another piece of fruit. Both pieces of fruit are apples. 6) There are thirteen shirts in your closet, seven blue and six green. You randomly select one to wear on Monday and then a different one on Tuesday. You wear blue shirts both days. 7) You select two cards from a standard shuffled deck of 52 cards. Both selected cards are diamonds. (Note that 13 of the 52 cards are diamonds.) 8) There are twelve shirts in your closet, seven blue and five green. You randomly select one to wear on Monday and then a different one on Tuesday. You wear a blue shirt on Monday and a green shirt on Tuesday. 9) There are six nickels and five dimes in your pocket. You randomly pick a coin out of your pocket and then return it to your pocket. Then you randomly pick another coin. The first coin is a nickel and the second coin is a dime. 10) A cooler contains fourteen bottles of sports drink: eight lemon-lime flavored and six orange flavored. You randomly grab a bottle and give it to your friend. Then, you randomly grab a bottle for yourself. Your friend gets a lemon-lime and you get an orange. k `2\0w1F8X WKcuZtnam TSqoHfjtSwiaKruee ILfLxCx.p U PAblNll _railglhjtysz KrMeIsaeXrtvzexdM.a n emlaudcec YwIijt`hK kisnmfeipnsirtuex qa\lagmebbjrra] ]2d. -1- Worksheet by Kuta Software LLC
11) A bag contains four red marbles and four blue marbles. Another bag contains seven green marbles and six yellow marbles. You randomly pick one marble from each bag. One marble is blue and one marble is yellow. 12) A basket contains four apples and seven peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit. The first piece of fruit is an apple and the second piece is a peach. 13) You flip a coin twice. The first flip lands heads-up and the second flip also lands heads-up. 14) There are eight nickels and eight dimes in your pocket. You randomly pick a coin out of your pocket and place it on a counter. Then you randomly pick another coin. The first coin is a nickel and the second coin is a dime. 15) A bag contains eight red marbles and seven blue marbles. You randomly pick a marble and then pick a second marble without returning the marbles to the bag. Both marbles are red. 16) A cooler contains thirteen bottles of sports drink: five lemon-lime flavored and eight orange flavored. You randomly grab a bottle and give it to your friend. Then, you randomly grab a bottle for yourself. You and your friend both get lemon-lime. 17) There are four nickels and seven dimes in your pocket. You randomly pick a coin out of your pocket and place it on a counter. Then you randomly pick another coin. The first coin is a nickel and the second coin is a dime. 18) You flip a coin and then roll a fair six-sided die. The coin lands tails-up and the die shows an odd number. 19) There are fourteen shirts in your closet, eight blue and six green. You randomly select one to wear on Monday and then a different one on Tuesday. You wear blue shirts both days. 20) A cooler contains twelve bottles of sports drink: four lemon-lime flavored and eight orange flavored. You randomly grab a bottle and give it to your friend. Then, you randomly grab a bottle for yourself. Your friend gets a lemon-lime and you get an orange. ^ B2I0r1k8V IKIuStYaL rsxoyfqtcwwagrve[ flllnck.o b vaolplp jrbitgqhltysv YreeJsYeXrpvDeTdO.p Y vmnajdreu uweiktmht PIbnRfhi_n`iKtDeU jailigoegbqrlab T2e. -2- Worksheet by Kuta Software LLC