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.

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 more than one but less than $2 \mathrm{m}$ away from his starting point.

Millie is playing in a cricket match and a game of hockey at the weekend. The probability that her team will win the cricket match is $0.75$ and the probability of her team winning the hockey match is $0.85$. What is the probability that Millies' team loses both matches?

Three events $A, B$ and $C$ are such that $A$ and $B$ are mutually exclusive and $\mathrm{P}\left(A\right)=0.2,\mathrm{P}\left(C\right)=0.3,\mathrm{P}(A\cup B)=0.4$ and $\mathrm{P}(B\cup C)=0.34$.

Calculate $P\left(B\right)$ and $\mathrm{P}(B\cap C)$.

Three events $A, B$ and $C$ are such that $A$ and $B$ are mutually exclusive and $\mathrm{P}\left(A\right)=0.2,\mathrm{P}\left(C\right)=0.3,\mathrm{P}(A\cup B)=0.4$ and $\mathrm{P}(B\cup C)=0.34$.

Determine whether $B$ and $C$ are independent.

Muamar tosses a coin and rolls a six-sided dice. Find the probability that Muamar gets a head on the coin, and does not get a $6$ on the dice.