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.

Find the number of elements of the sample space when two dices are rolled.

A box contains 1 black and 8 white balls. Find the probability of getting two same colours if replacement does not occur. Answer to two decimal places.

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.

A fair die is tossed 600 times.   How many numbers divisible by 3 are expected?

Nancy and Michael play a game in which the winner is the first to toss ahead with an unbiased coin. Nancy tosses first; Michael has the second and third tosses. If the first three tosses are all tails the game is drawn. Find the probability that Nancy wins and the probability that Michael wins. Is this game for both players?

Estimate the mean of the data.

\( \begin{array}{|c|c|c|c|c|c|} \hline
Class & 200 \le x \lt 300 & 300 \le x \lt 400 & 400 \le x \lt 500 & 500 \le x \lt 600 & 600 \le x \lt 700 \\ \hline
Frequency (f) & 21 & 23 & 29 & 35 & 17 \\ \hline
\end{array} \)

Describe the relationship between two variables.

Find the median of the scores.

\( \begin{array}{|c|c|} \hline
Score & Frequency \\ \hline
10 & 3 \\ \hline
20 & 8 \\ \hline
30 & 10 \\ \hline
40 & 15 \\ \hline
\end{array} \)

If the equation of the line of best fit is \(y = mx + b\), find \(m\) and \(b\).