Practice QUIZ1 and its solutions

Practice QUIZ1 and its solutions - =-= 1 2 9 10 2 1 1 6 7 8...

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AMS310.01 Practice quiz 1 1. If there are 10 people in a class and 8 will pass. How many sets of 8 people are there? 2. P(A) = 0.8 , P(B) = 0.4 , P(A B)= 0.3. P(A B) =____. 3. Suppose we toss a single die and the result is the number of dots observed. Then S={1,2,3,4,5,6}. Let A= {an even number of dots}, and let B={ the number of dots is less than 4} Then A B = __________. 4. At entry to the university 30% of a class declared themselves as computer science majors whereas 20% of the class graduated with a computer science major, and 10% (0.10) of the class both declared themselves as computer science majors at entry to the university and graduated with the computer science major. What percentage of the class both declared themselves at entry as computer science majors and did not graduate with a computer science major.? Answers 1. 45 2. 0.9 3. {1,3 } 4. 0.20 Solutions: 1. We are taking combinations (not arrangements) of r=8 from n=10 . So (n-r)=2 and the answer n C r = 10 C 2 = = = = = - = 1 2
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Unformatted text preview: =-= 1 2 9 10 2 1 1 .... 6 7 8 1 .... 7 8 9 10 ! 2 ! 8 ! 10 )! ( ! ! x x x x x x x x x x x r n r n 45 2. P(A ∪ B ) = P(A) + P(B) – P(A ∩ B) = 0.8 + 0.4 – 0.3 = 0.9. 3. { A } ={2, 4, 6}, { B} ={1, 2, 3} SO A = {1,3,5 } and A ∩ B = {1,3} 4. Let {E} denote {declare themselves computer science major at entry}, {G} denote event that a student {Graduates as a computer science major}. Given : P(E)=0.30 P(G)=0.20 and P(E ∩ G) = 0.10. We want P( G E ∩ ). Now P(E)= P(E ∩ G) +P( G E ∩ ). So 0.30 = 0.10 +P( G E ∩ ) . So P( G E ∩ ) = 0.30-0.10= 0.20. Or using the 2 x 2 table of probabilities and fact that P( A ) = 1- P(A) and P(A ∩ B )=P(A) - P(A ∩ B)we have P( G E ∩ ) = 0.2 . (bold =given) (not bold= calculated) UNDERLINED = question 4 calculation. {G} { G } Marginal probability E 0.1= = P(E ∩ G) 0.2= (0.3 - 0.1) =P(E ∩ G ) 0.3 = P(E) E 0.1 = ( 0.2 - 0.1 ) = P( E G) 0.6 =(0.7 - 0.1) = P( E G ) (1.0 - 0.3) = P( E ) Marginal Probability 0.2 = P(G) (1.0 - 0.2) = 0.8 =P( G ) 1.0 =P(S)...
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