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.

Given  \(P\left( A \right) = \dfrac{1}{2}\) and \(P\left( B \right) = \dfrac{1}{3}\),   find  \(P\left( {A\text{ and }B} \right)\),   correcting to one decimal place.

The probability of passing English, Chemistry and Biology are 0.7, 0.8 and 0.6 respectively. Assuming the exam results are independent, find the probability of passing at least English and Chemistry.

There is an 80% chance that Ben passes his driving test and a 90% chance that Amy passes hers. Find the probability that Amy passes.

The Venn diagram below shows the number of students in group \(A\), \(B\) or \(C\).   Find the number of students who are in either group \(A\) or \(B\).

State the following data as categorical or numerical.

the items students eat for lunch

A phone survey conducted for an insurance company rings \( 500 \) households between 11 am to 2 pm to ask what insurance company they prefer. State the intended population.

The mean of a set of five scores is \( 68 \). What is the new mean of the set of scores after a score of \( 20 \) is added?

What is the age of the child who is 35 kg?

Describe the strength of the linear relationship with correlation coefficient \(r = – 0.3\).