Karen Morrison and Nick Hamshaw Solutions for Exercise 4: Examination practice

Kiah plays a game. The game involves throwing a coin onto a circular board. Points are scored for where the coin lands on the board. If the coin lands on part of a line or misses the board then $0$ points are scored. The table shows the probabilities of Kiah scoring points on the board with one throw.

Find the value of $x$.

Kiah plays a game. The game involves throwing a coin onto a circular board. Points are scored for where the coin lands on the board. If the coin lands on part of a line or misses the board then $0$ points are scored. The table shows the probabilities of Kiah scoring points on the board with one throw.

Kiah throws a coin fifty times. Work out the expected number of times she scores $5$ points. 

Kiah plays a game. The game involves throwing a coin onto a circular board. Points are scored for where the coin lands on the board. If the coin lands on part of a line or misses the board then $0$ points are scored. The table shows the probabilities of Kiah scoring points on the board with one throw.

Kiah throws a coin two times. Calculate the probability that she scores either $5$ or $0$ with her first throw.

Kiah plays a game. The game involves throwing a coin onto a circular board. Points are scored for where the coin lands on the board. If the coin lands on part of a line or misses the board then $0$ points are scored. The table shows the probabilities of Kiah scoring points on the board with one throw.

Kiah throws a coin two times. Calculate the probability that she scores $0$ with her first throw and $5$ with her second throw.

Kiah plays a game. The game involves throwing a coin onto a circular board. Points are scored for where the coin lands on the board. If the coin lands on part of a line or misses the board then $0$ points are scored. The table shows the probabilities of Kiah scoring points on the board with one throw.

Kiah throws a coin two times. Calculate the probability that she scores a total of $15$ points with her first two throws.

Kiah plays a game. The game involves throwing a coin onto a circular board. Points are scored for where the coin lands on the board. If the coin lands on part of a line or misses the board then $0$ points are scored. The table shows the probabilities of Kiah scoring points on the board with one throw.

Kiah throws a coin three times. Calculate the probability that she scores a total of $10$ points with her three throws.

Dan either walks or cycles to school. The probability that he cycles to school is $\frac{1}{3}$. Write down the probability that Dan walks to school. 

Dan either walks or cycles to school. The probability that he cycles to school is $\frac{1}{3}$. There are $198$ days in a school year. Work out the expected number of days that Dan cycles to school in a school year.