The circular archery target shown, on which $1, 2, 3$ or $5$ points can be scored, is divided into four parts of unequal area by concentric circles. The radii of the circles are $3 \mathrm{cm}, 9 \mathrm{cm}, 15 \mathrm{cm}$ and $30 \mathrm{cm}$.

You may assume that a randomly fired arrow pierces just one of the four areas and is equally likely to pierce any part of the target.

Given that a total score of $6$ points is obtained with two randomly fired arrows, find the probability that neither arrow scores $1$ point.

Two ties are taken at random from a bag of three plain and five striped ties. Fiind the probability that both ties are:

plain

Two ties are taken at random from a bag of three plain and five striped ties. Find the probability that both ties are:

striped.

On a library shelf there are seven novels, three dictionaries and two atlases. Two books are randomly selected without replacement from these. Find the probability that the selected books are:

both novels

On a library shelf there are seven novels, three dictionaries and two atlases. Two books are randomly selected without replacement from these. Find the probability that the selected books are:

both dictionaries or both atlases.

A woman travels to work by bicycle $70\%$ of the time and by scooter $30\%$ of the time. If she uses her bicycle she is late $3\%$ of the time but if she uses her scooter she is late only $2\%$ of the time.

Find the probability that the woman is late for work on any particular day.

A woman travels to work by bicycle $70\%$ of the time and by scooter $30\%$ of the time. If she uses her bicycle she is late $3\%$ of the time but if she uses her scooter she is late only $2\%$ of the time.

Given that the woman expects not to be late on approximately $223$ days in a year, find the number of days in a year on which she works.

Two children are randomly selected from a group of five boys and seven girls. Determine which is more likely to be selected:

two boys or two girls?