Answer to Question #346339 in Statistics and Probability for dodo

Question #346339

2.1 Suppose P(A) = 0.75 and P(B) = 0.82. Find the following:


2.1.1 P (A and B) if A and B are independent. (2)


2.1.2 P (not A and not B), if A and B are independent. (2)


2.1.3 P (A and B), if A and B are mutually exclusive. (1)


2.2 Solve the following inequality. (3)


x2 - 5x + 6 ≥ 0


1
Expert's answer
2022-05-31T12:15:45-0400

2.1.1


P(AB)=P(A)P(B)P(A\cap B)=P(A)P(B)

=0.75(0.82)=0.615=0.75(0.82)=0.615

2.1.2


P(ACBC)=P(AC)P(BC)P(A^C\cap B^C)=P(A^C)P(B^C)

=(10.75)(10.82)=0.045=(1-0.75)(1-0.82)=0.045

2.1.3


P(AB)=0P(A\cap B)=0

2.2


x25x+60x^2 - 5x + 6 ≥ 0

(x2)(x3)0(x-2)(x-3)\ge0

x(,2][3,)x\in(-\infin, 2]\cup [3, \infin)


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