Presentation on theme: "What is Probability? The study of probability helps us figure out the likelihood of something happening. In math we call this “something happening” or."— Presentation transcript:
1 What is Probability?The study of probability helps us figure out the likelihood of something happening.In math we call this “something happening” or an “event”Probability is a way of expressing what the chances are that an event will occur
2 The term probability is common Weather forecast - 30 % chance of rainGambling - two dice will produce a sum of 7 is 1/6Things to know:1st thing:What the probability statements mean2nd thing:Then we consider how we determine the numerical value for that probability
3 1 2 3 4 5 6 Example: Number of ways 2 dice would produce a sum of 7 Die 1Die 2123456
4 36 different combinations Shows all the different ways the dice can landShows all the ways you could roll a seven6 of the 36 produce the sum of 7Must assume that each of the 36 combinations are equally likely to occurSo there is a 1/6 chance that you the sum of the dice will be 7
5 Example: Jar with 4 red marbles and 6 blue marbles Want to find the probability of drawing a red marble at random.Favorable outcome = drawing a red marble
6 Ways to Express Probability As a fraction~ 4/10 = 2/5As a decimal ~ 4/10 = .4As a percent ~ 4/10 = 40/100 = 40%Unlikely events have a probability near zeroLikely events have probabilities near 1
7 What is the total number of possible outcomes? Is called a sample spaceSample space is a set consisting of all the possible outcomes of an event.The number of different ways you can choose something from the sample space is the total number of possible outcomes.
8 We only have 2 events with our red and blue marbles Either we pick a red marble or a blue marbleIf you don’t do the first, then you must do the secondSo the probability of picking a red marble plus the probability of picking a blue marble equals 1 or 100%Sum = 4/10 + 6/10 = 10/10 = 1
9 So we have 4 red marbles and 6 blue marbles in our jar Sample space = all ten marblesbecause we are likely to draw anyone of themFavorable outcomes = # of red marbles = 4Possible outcomes = total # of marbles = 104/10 reduces to 2/5Probability of drawing a red marble where all outcomes are equally likely is 2/5(sample space)
10 When one event occurs:Probability of picking a red marble was 4/10 or 2/5Sample space = 10 marbles in the jarSo the probability of not picking a red marble1 = 10/1010/10 -4/10 = 6/10 or 3/5(this is also the probability of picking a blue marble)
11 When two events that are equally likely occur: You draw 1 marble from the 10Then I draw another marble from the nine that remainWhat is the probability that I will draw a blue one first?What is the probability that you will draw a red one second?
12 Your probability of drawing a blue one is 6/10 After you draw there are only 9 marbles left and 4 of those are red, so the probability that I will draw a red one is 4/9When there are 2 events, the second outcome is dependent on the first.
13 When two or more events occur that are not all equally likely: A. you draw a blue marble and then I draw a blue marble B. you draw a blue marble and then I draw a red marble C. you draw a red marble and then I draw a blue marble D. you draw a red marble and then I draw a red marble There are four possibilities but they are not all equally likely. Two separate events with the work “and”, there the outcome of the second is dependent on the outcome of the first we multiply.
14 Example A:Your probability of drawing a blue marble (6/10 = 3/5) X my probability of drawing another blue marble which would be 5/9
15 Example B:Your probability of drawing a blue marble (3/5) X my probability of drawing a red marble (4/9)
16 What can you learn from the chart? Classroom ExerciseWhat can you learn from the chart?
17 Average Distribution of Colors PlainPeanutCrispyDark ChocolatePeanut ButterAlmondbrown13121710red141520yellowgreen2423orange16blue