IB Mathematics Analysis and Approaches Topic SL…

Events $A$ and $B$ are such that $P(A)=0.4$ , $P(B)=0.7$ and $P(A\cup B)=0.8$ .

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

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

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

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

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}

A box contains two types of biased coins. One coin is drawn at random and tossed $n=8$ times.

With probability $0.4$ , a Type A coin is drawn; for Type A, the probability of heads on any toss is $p_A=0.35$ .

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

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

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

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

the value of the constant $k$ .

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

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

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

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

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

Write down the conditional distributions of $X\mid A$ and $X\mid B$ . Hence find $P(X=3)$ .

Use the laws of total expectation and total variance to find $E(X)$ and $\mathrm{Var}(X)$ .

The experiment resulted in exactly $6$ heads ( $X=6$ ). Compute $P(B\mid X=6)$ .

A game pays € $g(x)=2x-9$ . Decide whether to play before observing any tosses.

After observing that the first two tosses are both heads, you are offered the option to play the game (where the payoff $g(X)$ depends on the total number of heads $X$ in the $8$ tosses). Compute $E[g(X)\mid \text{first two are heads}]$ and decide whether to play.

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