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What the Brain Tells Us

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Submitted By DERWAR
Words 367
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Probability exercise 1. The probability of success, that is a win, is 4/9.
The assumptions made are i) The probability of getting any of the numbers is 1/9. ii) The wheel containing the numbers is unbiased. iii) The probability of getting any number is independent. 2. i) The sample space is 6*5=30. The list outcomes in the sample space is Ω={12,13,14,15,16,21,23,24,25,26,31,32,34,35,36,41,42,43,45,46,51,52,53,54,56,61,62,63,64,65} where the first digit represents the first ball to pick while the second digit represents the second ball to be picked. ii) When the first ball is replaced before the second ball is picked, then the sample space is given by 6*6=30. The list of outcomes in the sample space becomes Ω={11,12,13,14,15,16,21,22,23,24,25,26,31,32,33,34,35,36,41,42,43,44,45,46,51,52,53,54,55,56,61,62,63,64,65,66} 3. i) ABc means the elements that appear both in A and the complement of B. Hence ABc= ᶉ1. ii) BAc means the elements that appear both in B and the complement of A. Hence BAc=ᶉ3 iii) AB means the elements in both A and B. Hence AB=ᶉ2 iv) AUB means the elements that appear in A, B or both. Hence AUB=ᶉ1,ᶉ2,ᶉ3 4. a) Probability of A∩C =Φ which is the null set. This is because the no elements are I both A and C.
b) Probability of AUBUC= {1, 2, 3, 4, 5, 6}. This is because the union of all the events A, B, C gives the sample space, Ω.
5. i) Pr(Σ is 7ІΣ=odd)=Pr(Σ=7∩Σ=odd) divided by Pr(Σ=odd)= 19∕1=19 ii) Pr(Σ>10ӀN>7) =Pr(Σ>10∩N>7) divided by Pr(N>7)= 19∕39=1/3 iii ) Pr(Σ=oddӀN>8)=Pr(Σ=odd∩N>8) divided by

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