Conditional Probability and Transformations Quiz

Given two events <katex latex="A"></katex> and <katex latex="B"></katex> with <katex latex="P(A) = 0.4"></katex>, <katex latex="P(B) = 0.5"></katex>, and <katex latex="P(A \cap B) = 0.2"></katex>, what is <katex latex="P(A|B)"></katex>?

• <katex latex="0.2"></katex>

• <katex latex="0.4"></katex>

• <katex latex="0.5"></katex>

• <katex latex="0.6"></katex>

If <katex latex="P(A) = 0.3"></katex>, <katex latex="P(B) = 0.6"></katex>, and <katex latex="P(A \cap B) = 0.18"></katex>, what is <katex latex="P(A \cup B)"></katex>?

• <katex latex="0.48"></katex>

• <katex latex="0.72"></katex>

• <katex latex="0.78"></katex>

• <katex latex="0.88"></katex>

A point <katex latex="(2, 3)"></katex> is rotated <katex latex="90^\circ"></katex> counterclockwise about the origin. What are the coordinates of the image?

• <katex latex="(3, 2)"></katex>

• <katex latex="(-3, 2)"></katex>

• <katex latex="(-2, 3)"></katex>

• <katex latex="(-3, -2)"></katex>

What is the result of translating the point <katex latex="(4, -1)"></katex> by the vector <katex latex="(2, 5)"></katex>?

• <katex latex="(6, 4)"></katex>

• <katex latex="(2, 4)"></katex>

• <katex latex="(6, -6)"></katex>

• <katex latex="(2, -6)"></katex>

If a point <katex latex="(x, y)"></katex> is reflected over the <katex latex="y"></katex>-axis, what are the coordinates of its image?

• <katex latex="(x, -y)"></katex>

• <katex latex="(-x, y)"></katex>

• <katex latex="(-x, -y)"></katex>

• <katex latex="(y, x)"></katex>

Given <katex latex="P(A|B) = 0.7"></katex> and <katex latex="P(B) = 0.5"></katex>, what is <katex latex="P(A \cap B)"></katex>?

• <katex latex="0.35"></katex>

• <katex latex="0.7"></katex>

• <katex latex="0.2"></katex>

• <katex latex="0.5"></katex>

If <katex latex="P(A) = 0.5"></katex>, <katex latex="P(B) = 0.4"></katex>, and <katex latex="A"></katex> and <katex latex="B"></katex> are mutually exclusive, what is <katex latex="P(A \cup B)"></katex>?

• <katex latex="0.2"></katex>

• <katex latex="0.4"></katex>

• <katex latex="0.5"></katex>

• <katex latex="0.9"></katex>

A triangle with vertices <katex latex="(1, 2)"></katex>, <katex latex="(3, 2)"></katex>, and <katex latex="(2, 4)"></katex> is rotated <katex latex="180^\circ"></katex> about the origin. What are the coordinates of the image of <katex latex="(1, 2)"></katex>?

• <katex latex="(-1, -2)"></katex>

• <katex latex="(2, 1)"></katex>

• <katex latex="(-2, -1)"></katex>

• <katex latex="(1, -2)"></katex>

What is the image of the point <katex latex="(-2, 5)"></katex> after a translation by the vector <katex latex="(3, -4)"></katex>?

• <katex latex="(1, 1)"></katex>

• <katex latex="(5, 9)"></katex>

• <katex latex="(-5, 9)"></katex>

• <katex latex="(1, 9)"></katex>

If a point <katex latex="(4, -7)"></katex> is reflected over the <katex latex="x"></katex>-axis, what are the coordinates of its image?

• <katex latex="(-4, 7)"></katex>

• <katex latex="(4, 7)"></katex>

• <katex latex="(-4, -7)"></katex>

• <katex latex="(7, 4)"></katex>