hw2 - Math3C HW#2 wangyan@math.ucla.edu...

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wangyan@math.ucla.edu wenhuagao@math.ucla.edu Exercise 1 Page805 Ex5 Solution: A [ B = f 1 ; 2 ; 3 ; 5 g ; A \ B = f 1 ; 3 g : Exercise 2 Page805 Ex6 Solution: A c = f 2 ; 4 ; 6 g ; ( A c ) c = f 1 ; 3 ; 5 g = A: Exercise 3 Page805 Ex8 Solution: Since A \ B = f 1 ; 3 g ; A and B are not disjoint. Exercise 4 Page805 Ex12 Solution: Since A [ B ) P ( A [ B ) = 1 : Exercise 5 Page805 Ex13 Solution: P ( A c \ B c ) = P (( A [ B ) c ) = 0 : 2 ) P ( A [ B ) = 1 P (( A [ B ) c ) = 0 : 8 Since P ( A [ B ) = P ( A ) + P ( B ) P ( A \ B ) ) P ( B ) = P ( A [ B ) P ( A ) + P ( A \ B ) = 0 : 8 & 0 : 4 + 0 : 1 = 0 : 5 : Exercise 6 Page805 Ex14 Solution: Since P ( A [ B ) = P ( A ) + P ( B ) P ( A \ B ) P ( A \ B ) = P ( A ) + P ( B ) P ( A [ B ) = 0 : 4 + 0 : 4 & 0 : 7 = 0 : 1 P ( A c \ B c ) = P (( A [ B ) c ) = 1 P ( A [ B ) = 1 & 0 : 7 = 0 : 3 : Exercise 7 Page805 Ex17 Solution: f HH;HT;TH;TT g at least one head is f HH;HT;TH g ) The probability is : 3 4 : Exercise 8
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hw2 - Math3C HW#2 wangyan@math.ucla.edu...

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