## Are you ready to take your first step toward achieving your goal?

- 10 diagnosis quiz questions
- 10 minutes in duration
- Required to attempt all questions
- A mixture of short answer and multiple-choice questions
- Instant feedback straight after the test

## OK, let’s get started now!

## Are you ready to take your first step toward achieving your goal?

- Ten diagnosis quiz questions
- Ten minutes in duration
- Required to attempt all questions
- A mixture of short-answer and multiple-choice questions
- Instant feedback straight after the quiz

## OK, let’s get started now!

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- Question 1 of 10
##### 1. Question

A six-sided biased die is rolled 20 times and the number appearing uppermost is noted each time. The numbers uppermost on the six-sided die are:

\(4{\rm{ }}1{\rm{ }}6{\rm{ }}3{\rm{ }}5{\rm{ }}1{\rm{ }}4{\rm{ }}6{\rm{ }}3{\rm{ }}2{\rm{ }}5{\rm{ }}1{\rm{ }}6{\rm{ }}5{\rm{ }}2{\rm{ }}4{\rm{ }}2{\rm{ }}3{\rm{ }}5{\rm{ }}2\)

Estimate the experimental probability of rolling a “five” or “six” with this die.

Experimental probability =

CorrectIncorrect##### Hint

\(\text{Experimental probability } = \dfrac{{\text{favourable outcomes }}}{{\text{total number of trials }}}\)

- Question 2 of 10
##### 2. Question

The digits 1, 3, 5, 8 are drawn at random without replacement to form a four-digit number. Find the probability that the number is divisible by 5. Answer in decimal form.

CorrectIncorrect - Question 3 of 10
##### 3. Question

Given \(P\left( A \right) = \dfrac{1}{2}\) and \(P\left( B \right) = \dfrac{1}{3}\), find \(P\left( {\text{neither}\;A\;\text{nor}\;B} \right)\), correcting to one decimal place.

CorrectIncorrect - Question 4 of 10
##### 4. Question

Choose the best description of the grid shown below.

CorrectIncorrect - Question 5 of 10
##### 5. Question

The probability that a door is unlocked is 0.1. Only one of the five keys will unlock the door she wishes to enter. She only has time to try one key. Find the probability that she will not be able to get into the room.

CorrectIncorrect - Question 6 of 10
##### 6. Question

Find the financial expectation of a ticket in a raffle. The raffle has 500 tickets and there is one prize worth 200 dollars.

dollar(s)

CorrectIncorrect - Question 7 of 10
##### 7. Question

Let \(X\) represent the discrete random variable ‘number of tails’ obtained in two coin tosses. Find the possible values of \(X\).

CorrectIncorrect - Question 8 of 10
##### 8. Question

Find \(P\left( {X > 2} \right)\).

\( \begin{array} {|c|c|c|c|c|c|} \hline

x & 0 & 1 & 2 & 3 & 4 \\ \hline

P( X = x ) & 0.2 & 0.3 & 0.2 & 0.1 & 0.2 \\ \hline

\end{array} \)CorrectIncorrect - Question 9 of 10
##### 9. Question

A fair coin is tossed 4 times. If \(X \) represents the number of tails obtained, find \(E\left( X \right)\).

CorrectIncorrect - Question 10 of 10
##### 10. Question

\(\begin{array} {|c|c|c|c|} \hline

&iPhone &Samsung &no \ phone \\ \hline

Year \ 7 &26 &21 &9 \\ \hline

Year \ 8 &38 &22 &4 \\ \hline

Year \ 9 &42 &35 &3 \\ \hline

\end {array} \)Find the probability that a randomly chosen student uses iPhone. Answer in decimal form.

CorrectIncorrect