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The Beginning: Experimental Probability: Your actually doing to experiment, P(E)= ___ #of times event occurs____total number of times the experiment is repeated. Ex. Suppose you flipped a coin 30 times and tails shows 19 times. The outcome are H or T and the event E=tails. P(tails)=19/30 Subjective: estimate of the event based on intuition and experince. Theoritcal: based on mathematical laws by fair objects or experiments. P(A)=n(A)/n(S)Probability of an event is A. And S is the sample space. Complementary Events: the complement of a set A is written as A and consists of all the outcomes in the sample space that are not in A. Ex. rolling 1 die sample space={1,2,3,4,5,6} If the event A= rolling a 4 than P(A)=1/6 and A=not rolling a 4 then P(A)=5/6.
Amanda's Math Blog
Idependent Events: Events that have no effect upon one another. Ex student has poor hearing, a student has blond hair. Dependent Events: Events where that has one effect on the next. Ex well trained worker, worker meets production quota. Mutually Exclusive Events: Two event sets th at have no outcomes in common. Ex Probability of rolling a 3 or a 5. A={3,5} or A={3} B={5} P(A)=1/6 and P(B)=1/6 Formula for Mutually Exclusive: P(A or B) =P(A)+P(B) P(A or B) 1/6+1/6=1/3 Nonmutually Exclusive Events: Events that can occur at the same time. P(AUB)= P(A)+P(B)-P(AnB)
Conditional Probability: B is occuring given that event A has already occured. Formula: P(B|A) =(B and A)/A Ex. The probability that it is friday and that a student is absent is 0.03. Since there are 5 school days in a week, the probability that it is Friday is 0.2. What is the probability that student is absent given that today is Friday? P(Absent|Friday)=P(Friday and Absent)/P(Friday) =0.03/0.2 =0.15 x100 =15%
Permutations: has to be in order to solve Ex. Inarranging seven students to sit in the front row for a class picture. How many possible arrangements of the seven students are there? 7x6x5x4x3x2x1=5040 ways of arranging the students. Ex2:P(8,3) P(8,3)=8!/(8-3)! =8!/5! =8x7x6x5/5 =8x7x6=336
Combinations: Doesn't have to be in order. Art, Beth, Carl, Deliah and Ellie are running for SAC postions President,Vice-President and Secretary. How many ways can the three positions be filled? Does order matter? 5C3=5!/(5-3)! 3! =5!/2!(3)! =5x4x3/2!(3)! 5x4=20/2 =10
And is mulitply Or is add!
Pascals Triangle: 1 1 1 1 2 2 1 Find the sum of 2^16 =65536 Express as a single term: t3,2=t2,1+t2,2
