The two spinners shown are used in a game.

Each arrow is spun once. The score is the total of the two numbers shown by the arrows.
A table is drawn up to show all scores that can be obtained in this game.

1. What is the value of \(X\) in the table?  (1 mark)

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2. What is the probability of obtaining a score less than 4?  (1 mark)

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3. On Spinner \(B\), a 2 is obtained. What is the probability of obtaining a score of 3?  (1 mark)

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Two unbiased dice,  \(A\)  and  \(B\), with faces numbered  \(1\),  \(2\),  \(3\),  \(4\),  \(5\) and  \(6\) are rolled.

The numbers on the uppermost faces are noted. This table shows all the possible outcomes.

 
\begin{align}
\textbf{Die B } \
\begin{array}{c }
\textbf{Die A } \\
\begin{array}{c|c|c|c|c|c|c}
\ & 1 & 2 & 3 & 4 & 5 & 6  \\
\hline
\ 1 & 1,1 & 1,2 & 1,3 & 1,4 & 1,5 & 1,6  \\
\hline
\ 2 & 2,1 & 2,2 & 2,3 & 2,4 & 2,5 & 2,6  \\
\hline
\ 3 & 3,1 & 3,2 & 3,3 & 3,4 & 3,5 & 3,6  \\
\hline
\ 4 & 4,1 & 4,2 & 4,3 & 4,4 & 4,5 & 4,6  \\
\hline
\ 5 & 5,1 & 5,2 & 5,3 & 5,4 & 5,5 & 5,6  \\
\hline
\ 6 & 6,1 & 6,2 & 6,3 & 6,4 & 6,5 & 6,6  \\
\end{array}
\end{array}
\end{align}

A game is played where the difference between the highest number showing and the lowest number showing on the uppermost faces is calculated.

What is the probability that the difference between the numbers showing on the uppermost faces of the two dice is one?   (2 marks)

In any standard six-sided dice, the sum of the opposite faces is 7.

Milo rolls 3 dice and the total of the top faces is 5.

What is the sum of the three opposite faces?  (2 marks)

Maxi and Jim are playing a dice game.

They have two standard 6-sided dice.

One of the die is white and the other is grey.

Maxi needs to roll a total of 11 to win.

There are two different ways she can roll a total of 11 as shown.
 
 

Jim has to roll a 6 to win.

How many different ways can Jim roll a total of 6?  (1 mark)

Bryce has a bag of marbles. 80% of his marbles are red.

Bryce takes a yellow marble from his bag and loses it in a game.

If he takes another marble from the bag without looking, what are the chances it is red?

1. greater than 80%
2. equal to 80%
3. less than 80%
4. there is not enough information to predict the chance

Luigi spins these two arrows. He then adds the numbers in the sections where the  arrows stop to get the total score.
 

 
How many different ways can Luigi get a total of 7?  (2 marks)