IFYMaths2BusinessProbability2.pptx
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1、Introduction to ProbabilityIntroduction to ProbabilityIntroduction to ProbabilityYou have calculated probabilities in GCSE work and used tree diagrams to solve some probability problems.We will now revise and extend probability work,starting with some definitions.An experiment or trial has a number
2、of outcomes.These are the results from the experiment or trial.An event is a particular result or set of results.We usually use the word event for the outcomes we are interested in.e.g.1.If I toss a coin,the possible outcomes are a head or a tail.I could define H as the event of getting a head.e.g.2
3、.If I roll a die,the possible outcomes are the numbers 1,2,3,4,5 or 6.An event could be getting an even number.Introduction to ProbabilityLets take the example of the die.When we roll the die,there are 6 possible outcomes,all equally likely,and these form the possibility space.You know that the prob
4、ability of the event“getting an even number”isTo see how we get this result formally,we need one more definition.For equally likely outcomes,the probability of an event,E,is given byThere are 3 even numbers and 6 possible outcomes so we get the answer 3 out of 6,or .P(E)=number of ways E can occurnu
5、mber of possible outcomesIntroduction to Probabilitye.g.1.Two dice are rolled and the sum of the numbers on the uppermost faces are added.What is the probability of getting a 7?Thinking about this we realise that we can get 7 in a number of ways.For example,1 on the 1st die and 6 on the 2nd or 2 on
6、the 1st and 5 on the 2nd.Also,what about 5 on the 1st and 2 on the 2nd?There are also other possibilities.These possibilities are equally likely so we can use the definition to find P(7)but its not easy to see in how many ways the event can arise.To solve this problem we can draw a possibility space
7、 diagram and the answer is then easy to see.Introduction to ProbabilitySolution:121110987111098761098765987654328765437654654321654321+1st die2nd dieWe now count the number of 7s.e.g.1.Two dice are rolled and the sum of the numbers on the uppermost faces are added.What is the probability of getting
8、a 7?Introduction to ProbabilitySolution:121110987111098761098765987654328765437654654321654321+1st die2nd dieWe now count the number of 7s.and divide by the total number of possibilities.So,e.g.1.Two dice are rolled and the sum of the numbers on the uppermost faces are added.What is the probability
9、of getting a 7?Introduction to Probability Outcomes are the results of trials or experiments.SUMMARYAn event is a particular result or set of results.A possibility space is the set of all possible outcomes.For equally likely outcomes,the probability of an event,E,is given byP(E)=number of ways E can
10、 occurnumber of possible outcomesIntroduction to ProbabilityExercise1.Two dice are rolled and the score is defined as the product of the numbers showing on the uppermost faces.Write out the possibility space and use it to find the probability of scoring 12 or more.2.Four coins are tossed.Write out t
11、he possibility space in the form of a list of all possible outcomes and use it to find the probability of 3 heads.Introduction to Probability1.Two dice are rolled and the score is defined as the product of the numbers showing on the uppermost faces.Write out the possibility space and use it to find
12、the probability of scoring 12 or more.Solution:3630241812630252015105242016128418151296321121086426543654321654321 1st die2nd dieP(12 or more)Introduction to Probability1.Two dice are rolled and the score is defined as the product of the numbers showing on the uppermost faces.Write out the possibili
13、ty space and use it to find the probability of scoring 12 or more.Solution:3630241812630252015105242016128418151296321121086426543654321654321 1st die2nd dieP(12 or more)Introduction to ProbabilitySolution:2.Four coins are tossed.Write out the possibility space in the form of a list of all possible
14、outcomes,for example,H,H,H,H,and use it to find the probability of 3 heads.H,H,H,HT,H,H,H H,T,H,H H,H,T,H H,H,H,TT,T,H,HT,H,T,HT,H,H,TH,T,T,HH,T,H,TH,H,T,TT,T,T,HT,T,H,TT,H,T,TH,T,T,TT,T,T,TIntroduction to ProbabilitySolution:P(3 Heads)2.Four coins are tossed.Write out the possibility space in the f
15、orm of a list of all possible outcomes,for example,H,H,H,H,and use it to find the probability of 3 heads.H,H,H,HT,H,H,H H,T,H,H H,H,T,H H,H,H,TT,T,H,HT,H,T,HT,H,H,TH,T,T,HH,T,H,TH,H,T,TT,T,T,HT,T,H,TT,H,T,TH,T,T,TT,T,T,TIntroduction to ProbabilityTree Diagrams1st chocolate2nd chocolateRNRNNRIntroduc
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