Answer to Question #346339 in Statistics and Probability for dodo

Question

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

Answer 1

2.1.1

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

$$=0.75(0.82)=0.615$$

2.1.2

$$P(A^C\cap B^C)=P(A^C)P(B^C)$$

$$=(1-0.75)(1-0.82)=0.045$$

2.1.3

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

2.2

$$x^2 - 5x + 6 ≥ 0$$

$$(x-2)(x-3)\ge0$$

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