Two tetrahedral dice, one blue and the other red, are each numbered $1$ to $4$ . The two dice are rolled and the results noted.

Draw a sample space diagram for this experiment. Find the probability that the sum of the numbers on the dice is a prime number.

A box contains three cards bearing the numbers $1,2,3$. A second box contains four cards with the numbers $2,3,4,5$. A card is chosen at random from each box.

Draw the sample space diagram for the experiment.

A box contains three cards bearing the numbers $1,2,3$. A second box contains four cards with the numbers $2,3,4,5$. A card is chosen at random from each box.

Draw the sample space diagram for the experiment. Find the probability that the cards have the same number.

A box contains three cards bearing the numbers $1,2,3$. A second box contains four cards with the numbers $2,3,4,5$. A card is chosen at random from each box.

Draw the sample space diagram for the experiment. Find the probability that the larger of the two numbers drawn is a $3$.

A box contains three cards bearing the numbers $1,2,3$. A second box contains four cards with the numbers $2,3,4,5$. A card is chosen at random from each box.

Draw the sample space diagram for the experiment. Find the probability that the sum of the two numbers on the card is less than $7$.

A box contains three cards bearing the numbers $1,2,3$. A second box contains four cards with the numbers $2,3,4,5$. A card is chosen at random from each box.

Draw the sample space diagram for the experiment. Find the probability that the product of the numbers on the card is at least $8$.

A box contains three cards bearing the numbers $1,2,3$. A second box contains four cards with the numbers $2,3,4,5$. A card is chosen at random from each box.

Draw the sample space diagram for the experiment. Find the probability that at least one even number is chosen.

Toby plays a game with a dice called "Come and Go". He rolls the dice. If the score is $1$ he moves forward $1 \mathrm{m}$. If the score is $2$ he moves right $1 \mathrm{m}$. If the score is $3$ he moves backwards $1 \mathrm{m}$. If the score is $4$ he moves left $1 \mathrm{m}$. If the score is a $5$ or $6$ he stays where he is. Toby rolls the dice twice. What is the probability that he is at the same point where he started.

Toby plays a game with a dice called "Come and Go". He rolls the dice. If the score is $1$ he moves forward $1 \mathrm{m}$. If the score is $2$ he moves right $1 \mathrm{m}$. If the score is $3$ he moves backwards $1 \mathrm{m}$. If the score is $4$ he moves left $1 \mathrm{m}$. If the score is a $5$ or $6$ he stays where he is. Toby rolls the dice twice. What is the probability that he is exactly $2 \mathrm{m}$ away from his starting point.