IB Mathematics Analysis and Approaches Topic SL…

Events $A$ and $B$ are such that $P(A)=0.4$ , $P(B)=0.7$ and .

(a) the value of $P(A\cap B)$ .

(b) Find the value of $P(A'\mid B')$ .

(e) Compute $P(10\le Y\le 20)$ .

(f) Find $P(X>6\mid X>3)$ and give your answer in exact form.

Events $A$ and $B$ are such that $P(A) = 0.4$ , $P(B) = 0.6$ and $P(A \cup B) = 0.8$ .

(b) Find the value of $P(A' \mid B')$ .

Events $A$ and $B$ are such that $P(A) = 0.7$ , $P(B) = 0.5$ and $P(A \cup B) = 0.9$ .

(b) Find the value of $P(A' | B')$ .

A continuous random variable $X$ has probability density function

f(x)=\begin{cases} k\,x\,e^{-x/3},& x\ge 0,\\ 0,& x<0. \end{cases}

(b) Find $E(X)$ and $\mathrm{Var}(X)$ .

(c) Show that the mode of $X$ is $3$ . Then, by solving $\displaystyle \int_{0}^{m} f(x)\,dx=\tfrac12$ , find the median $m$ correct to three significant figures (calculator required).

(d) Let $Y=2X+5$ . Find $E(Y)$ and $\mathrm{Var}(Y)$ .

A manufacturing plant makes two models of components: Model X and Model Y. The probability that a component is Model X is 0.75. For a Model X component, the probability that it is defective is 0.08; for a Model Y component, the probability that it is defective is 0.16. A quality control test is applied to components, and when a component is defective, the test identifies it with probability 0.8; when it is not defective, the test gives a false positive result with probability 0.05.

(a) a tree diagram showing the probabilities for component model, defect status, and test result.

(b) Find the probability that a randomly chosen component gives a positive defect test.

(d) if the events "the component is defective" and "the component tests positive" are independent.

(a) the value of $P(A \cap B)$ .

(a) the value of the constant $k$ .

(a) the value of $P(A \cap B)$ .

IB Mathematics Analysis and Approaches SL 4.11—conditional and Independent Probabilities, Test for Independence Questionbank

IB Mathematics Analysis and Approaches SL 4.11—conditional and Independent Probabilities, Test for Independence Questionbank

IB Mathematics Analysis and Approaches SL 4.11—conditional and Independent Probabilities, Test for Independence Questionbank

IB Mathematics Analysis and Approaches SL 4.11—conditional and Independent Probabilities, Test for Independence Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 4.11—conditional and Independent Probabilities, Test for Independence Questionbank