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Instructions
1.
2.
3.
You will initially be given a set
of questions of ‘Level 1’
difficulty.
Once you’ve completed these
questions, put your hand up,
I’ll check your answers to see
they’re mostly correct, then
give you the next level up.
You may work in pairs.
Some questions require you to use the
rules of independence and mutual
exclusivity. Others might require you to
think about the sample space.
Example
Two boys apply to Tiffin. Bob has
a 0.3 chance of getting in. Martin
has a 0.4 chance of getting in.
Calculate the probability that
neither boy gets in.
P(neither get in) = 0.7 x 0.6 = 0.42
Answer Sheet
Level 1
Level 2
Q1
Q1
Q2
Q2
Q3
Q3
Q4
Q4
Q5
Q5
Q6
Q6
Q7
Q7
Level 3
Q1
Q4
Q2
Q5
Q3
QN
Level 1
Q1
Q2
I pick a card from a pack at
random, then put it back, then
shuffle and pick another.
What’s the probability I get 2
Kings?
Q3
I have two dice and a pack of
cards. What’s the probability
that I roll two 6s and get a club?
Q4
I toss two coins. What’s the
probability I get exactly 1 Head?
I toss two coins. What’s the
probability I get two heads or
two tails?
Level 1
Q5
Q6
I have a 30% probability of
getting gold at IMC. My friend
has a 60% chance. What’s the
probability that I get gold but
he doesn’t?
Q7
I throw two dice. What’s the
probability the sum is greater or
equal to 10?
I throw two dice. What’s the
probability I get two 2s, two 3s
or two 5s?
Level 2
Q1
Q2
Gladys has a 60% chance of
getting a Distinction in Extreme
Granny Surfing. Mildred has a
30% chance. What’s the
probability that just one of
them gets a Distinction?
Q3
I roll two dice. What’s the
probability I get a 1 and a 2?
Q4
I have 3 yellow marbles, 2
green and 1 red. Dave picks a
marble (without moving it).
Max then picks one. What’s the
probability that they pick the
same colour?
I pick a card without putting it
back. Then John picks one from
the same pack. What’s the
probability we both get Kings?
Level 2
Q5
Q6
I have the letters ‘A’, ‘T’ and ‘C’
printed on 3 cards, and a
monkey randomly arranges
them in a line. What’s the
probability it spells ‘CAT’?
Q7
If I throw two dice, what’s the
probability I get a 1 and 2, or a
3 and 4, or a 5 and a 6.
Now, I have 4 cards with the
letters ‘C’, ‘A’, ‘H’ and ‘T’, and a
French monkey. If it again
randomly puts the letters in a
line, what’s the probability I get
the word ‘CHAT’?
Level 3
Q1
Q2
Michael’s Ferrari has a 60% chance
of breaking down this year. Tom’s
Aston Martin has a 50% chance of
breaking down. And Prannay’s
BMW has a 40% chance. What’s
the probability that exactly two
cars break down?
Q3
I toss 10 coins. What’s the
probability that I get between 1
and 9 heads?
Q4
I have 3 yellow marbles, 2
green and 1 red. Ian picks a
marble and doesn’t put it back.
Mark then picks one. What’s
the probability that they pick
the same colour now?
Now a Finnish monkey arranges
the letters ‘S’, ‘K’, ‘S’, ‘I’ and ‘A’
in a line. What’s the probability
it spells the word KISSA?
Level 3
Q5
QN
I’m capture by insane mathematicians
and forced to play Russian roulette. I
have a gun with n slots in the barrel
and 1 bullet. I shoot, then if I survive,
I rotate the barrel randomly then
shoot again. I shoot n times. Give an
expression for the probability of me
surviving (in terms of n).
I have two shuffled packs of
cards on the table. I turn two
cards over at time. If the two
cards exactly match, I die
immediately, unless they’re the
last card of each pack. What’s
the probability that I survive?
Answers
Level 1
Level 2
Q1
1/169
Q1
27/50
Q2
1/144
Q2
1/18
Q3
1/2
Q3
7/18
Q4
1/2
Q4
1/221
Q5
3/25
Q5
1/6
Q6
1/12
Q6
1/24
Q7
1/6
Q7
3/18
Q1
19/50
Q4
1/60
Q2
1022/1024
Q5
(1-(1/n))n
Q3
4/15
QN
1/52
Level 3