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# hw2 - Math3C HW#2 [email protected]

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Math3C HW#2 [email protected] [email protected] 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 Page805 Ex19 1

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Solution: ° = ° 6 1 ± ° 6 1 ± = 36 only the °rst one is 4: 1 ± 5 = 5 only the second one is 4: 1 ± 5 = 5 both two are 4: 1 ± 1 = 1 The probability for at least one is 4: 5+5+1 36 = 11 36 : ° Exercise 9 Page805 Ex21 Solution: ° = ° 6 1 ± ° 6 1 ± = 36 First way:
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hw2 - Math3C HW#2 [email protected]

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