DP Mathematics: Applications and Interpretation Questionbank

Find an expression for $q$ in terms of $p$.

Find the value of $p$ which gives the largest value of $\text{E}\left(X\right)$.

Hence, find the largest value of $\text{E}\left(X\right)$.

Write down the value of $\underset{i=1}{\overset{9}{\text{Σ}}}{u}_i$.

Find the value of $u_1$.

A game is played in which the arrow attached to the centre of the disc is spun and the sector in which the arrow stops is noted. If the arrow stops in sector $1$ the player wins $10$ points, otherwise they lose $2$ points.

Let $X$ be the number of points won

Find $\text{E}\left(X\right)$.

Find the probability of scoring a six when rolling the novelty die.

a player scores at least $3$ in a game.

a player scores $6$, given that they scored at least $3$.

Complete the table to show the probability distribution of $T$.

Find the expected score of a game.

Jae Hee plays the game twice and adds the two scores together.

Find the probability Jae Hee has a total score of −3.

Find the exact value of $p$.

Calculate the expected score.

Find the value of a and the value of b.

Find the expected value of T.

Show that $a=\frac{2}{3}$.

Find .

Given that , and that 0.25 < s < 0.4 , find the value of s.

Find the value of $k$.

By considering the graph of f write down the mean of $X$;

By considering the graph of f write down the median of $X$;

By considering the graph of f write down the mode of $X$.

Show that $P(0⩽X⩽2)=\frac{1}{4}$.

Hence state the interquartile range of $X$.

Calculate $P(X⩽4|X⩾3)$.

Show that $a=32$ and $b=\frac{1}{12}$.

Find $\text{E}(X)$.

Find $\text{Var}(X)$.

Find the median of $X$.

Find $\text{E}(Y)$.

Find $\text{P}(Y⩾3)$.

Find the probability that on a randomly selected day, Steffi does not visit Will’s house.

Copy and complete the probability distribution table for Y.

Hence find the expected number of times per day that Steffi is fed at Will’s house.

In any given year of 365 days, the probability that Steffi does not visit Will for at most $n$ days in total is 0.5 (to one decimal place). Find the value of $n$.

Show that the expected number of occasions per year on which Steffi visits Will’s house and is not fed is at least 30.

One of the players is chosen at random. Find the probability that this player’s score was 5 or more.

Calculate the mean score.

Find the coordinates of the point of intersection of the planes defined by the equations $x+y+z=3,x-y+z=5$ and $x+y+2z=6$.

Complete the probability distribution table for $X$.

Find the expected value of $X$.

Determine the value of $\text{E}(X^2)$.

Find the value of $\text{Var}(X)$.

Find the value of $k$.

Write down $\text{P}(X=2)$.

Find $\text{P}(X=2|X>0)$.

Find the value of k.

Calculate the expected value of the score.

The die is rolled 80 times. On how many rolls would you expect to obtain a three?

Write down the value of k.

Show that μ = 106.

Find P(M < 95) .

Find the probability that a bag of apples selected at random contains at most one small apple.

Find the expected number of bags in this crate that contain at most one small apple.

Find the probability that at least 48 bags in this crate contain at most one small apple.

Find $k$.

Hence, find the probability that exactly $k$ students are left handed;

Hence, find the probability that fewer than $k$ students are left handed.

Write down the probability that the first disc selected is red.

Let $X$ be the number of red discs selected. Find the smallest value of $m$ for which .

Find the probability of rolling exactly one red face.

Find the probability of rolling two or more red faces.

Show that, after a turn, the probability that Ted adds exactly $10 to his winnings is $\frac{1}{3}$.

Write down the value of $x$.

Hence, find the value of $y$.

Ted will always have another turn if he expects an increase to his winnings.

Find the least value of $w$ for which Ted should end the game instead of having another turn.

Find the probability, in terms of $n$, that the game will end on her first draw.

Find the probability, in terms of $n$, that the game will end on her second draw.

third draw.

fourth draw.

Hayley plays the game when $n$ = 5. She pays $20 to play and can earn money back depending on the number of draws it takes to obtain a blue marble. She earns no money back if she obtains a blue marble on her first draw. Let M be the amount of money that she earns back playing the game. This information is shown in the following table.

Find the value of $k$ so that this is a fair game.

Find $q$.

Find $p$.

Write down the probability of drawing three blue marbles.

Explain why the probability of drawing three white marbles is $\frac{1}{6}$.

The bag contains a total of ten marbles of which $w$ are white. Find $w$.

Grant plays the game until he wins two prizes. Find the probability that he wins his second prize on his eighth attempt.

Jill plays the game nine times. Find the probability that she wins exactly two prizes.