1. You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble.
You pick a random bag and take out one marble.
It is a white marble.
What is the probability that the remaining marble from the same bag is also white?
The picture represents an area of parkland with a lawn (green) which is circular except for the area inside the lawn which is occupied by a smaller circular pond (blue). The dotted lines represent a diameter of the lawn.
If the pond’s surface area is 2 hectares, what is the area of the lawn?
3. What is 2% of 3% as a percentage?
4. In Colourland, the currency rate is 100 cents to the dollar.
However, the coinage is a bit unusual, in that there are only four denominations, yellow, red, green and blue.
From the examples on the right, work out the individual value of
(a) the green coin
(b) the blue coin
(c) the yellow coin
(d) the red coin
5. In the knock-out finals finals of a certain competition:
• Chelsea, who played and beat Norwich, won one more game than Watford.
• Southampton lost to the team that played Everton in the semi-finals.
• Arsenal won one more game than Liverpool.
• Everton, who won one more game than Arsenal, never met either Chelsea or Spurs.
(a) Who Won?
(b) Who eliminated Southampton in the quarter final?
(c) Which three other teams never got to the semifinals?
This solution grid might help.
7. At a Seniors Reunion, three couples now living in different cities of Australia renewed their friendship during a Dance. In the two dances recorded here, nobody danced with his or her spouse, and each had a different partner for each of the two dances. During a foxtrot, the partners were Andrew and the lady from Sydney, Flo’s husband and Mrs Gould, and Mr Hedges and Colin’s wife. In the waltz, Brian danced with the lady from Brisbane, Dolly’s husband danced with the lady from Perth, and Mr Jacobs partnered Edna. Name each couple and say what city they come from.
8. The picture below represents a Mastermind game. For those unfamiliar with Mastermind, the idea is for one player (the “code maker”) to set a code based on four colours in a row. The opponent, (the “code breaker”) has to crack the code in as few trials as possible. In this game, the codebreaker can crack the code after only five trials. The possible colours are yellow, green, black, orange red and purple. (Colours may be repeated – for example, red orange red, green would be possible).
After trial 1, the codebreaker is told that only one of his colours is correct, but it’s in the wrong place. In trial 2, he has two of the four colours correct, but both in the wrong position. In trial 3, two colours are correct, but only one is in the right place; and so on. Write the correct code.
9. Five cards have been laid out.
All are between Ace (1) and 10 in value.
No two cards have the same numerical value.
The total value of red cards is the same as the total value of the black cards.
The total value of Hearts is 12.
The even-value cards have a total four higher than the odd-value cards.
The Club has a lower value than the Spade.
The lowest card is a Diamond.
Which five cards have been dealt?