S1 Revision Notes and Questions – Probability
ANSWERS
2nd Level Questions
Describe the following events using the words: IMPOSSIBLE, UNLIKLEY, EVEN CHANCE,
LIKLEY and CERTAIN.
1. January will be the month before February. CERTAIN
2. Friday will follow Thursday. CERTAIN
3. Next year your birthday will be on the same date as it was this year. CERTAIN
4. If you threw a dice you will roll an even number. EVEN CHANCE
5. You will fly out the window. IMPOSSIBLE
6. When you are 30, you will be taller than you are now. LIKELY
7. You will be a millionaire when you get older. UNLIKELY
8. You will be famous one day. UNLIKELY
9. You will see some children in school. LIKELY
10. The government will make it compulsory for everyone to own an Xbox. UNLIKELY
3rd Level Questions
Q1. A die is rolled. Find the probability that it lands showing:
(a) 1
1/6
(b) an odd number 1/2
(c) a prime number 1/2
(d) a multiple of 3 1/3
(e) a number less than 3 1/3
Q2. A spinner has 5 edges as shown in the diagram. When it is spun it comes to rest on one
edge. What is the probability that it comes to rest on a number
a) less than 3? 2/5
b) Bigger than 1? 4/5
c) That is odd? 3/5
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Q3. A newsagent delivers these papers, one to each house.
Sun 200
Mirror 300
Telegraph 200
Times 120
Mail 100
Express 80
What is the probability that a house picked at random has:
a. the Times? 120/1000 = 3/25
b. the Mail?
100/1000 = 1/10
c. the Express? 80/1000 = 2/25
Q4. The letters in the word RABBIT are placed in a tub, and a letter taken at random. What is
the probability of taking out:
a) A letter T? 1/6
b) A letter B?
1/3
4th Level Questions
Q1. Darren and his friend are playing with a pack of cards from which his maths teacher has
confiscated the Ace of Spades and the King of Hearts. What is the probability that the first card
he deals is
(a) an Ace ? 12/50 = 6/25
(b) a black card 25/50 = 1/2
(c) a Queen 4/50 = 2/25
(d) the 4 of clubs?
1/50
(e) not a club? 37/50
Q2. A class is going to play three games. In each game some cards are put into a bag.
Each card has a square or a circle on it. If it is a circle, the girls will get a point. If it
is a square, the boys will get a point.
a. Which game are the girls most likely to win? Why? Game 3 as 8/12 = 2/3
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b. Which game are the boys most likely to win? Why? Game 2 as 8/8 = 1
c. Which game is impossible for the girls to win? Game 2 as certain boys will
win
e. Which game is it equally likely that the boys or girls win? Game 1 as ½ for
boys and girls
f. Are any of the games unfair? Why? Game 2 as girls cannot win.
Q3. In a computer ‘minefield’ game, ‘mines’ are hidden on grids. When you land
randomly on a square with a mine, you are out of the game.
a. The circles indicate where the mines are hidden on three different grids. On
which of the three grids is it hardest to survive? Grid 1= as 6/18 chance of
landmine, simplifying to 1/3
Grid 2 = 8/25 chance of landmine
Grid 3 = 7/20 chance of landmine, so GRID 3 is hardest to survive.
b. Grid 1 above is a 3 by 6 grid with 6 mines. On which of the following grids is it
hardest to survive?
X. 10 mines on an 8 by 8 grid 10/64 = 0.15625
Y. 40 mines on a 16 by 16 grid 40/256 = 0.15625
Z. 99 mines on a 30 by 16 grid 99/480 = 0.20625 HARDEST TO SURVIVE
Explain your reasoning.
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