Transcript Document

Welcome to…
Charlie’s
House of
Chance
A brand new reality T.V.
show where contestants
have the chance to win
£1,000,000.
At the beginning of the show there are
12 contestants in the house.
Each week, the contestants must
nominate other contestants for eviction.
One of the nominated contestants is
chosen at random by a computer and is
then evicted from the house.
The last contestant left in the
house wins the big money
prize.
The nominations for the first week are in.
The contestants up for eviction this week are:
Brian
Bryony
Brad
24
22
19
Bob
Brad
31
Bob
NorthernBryony
Brian
Scotland
Scotland
England
Ireland
19
Teacher
Vet
Psychologist
Mechanic
31
24
22
Northern Ireland
England
Scotland
Scotland
Mechanic
All the contestants up for eviction arePsychologist
nervous
– anyone
Teacher
Vet
could be chosen at random by the computer.
Can you help the contestants figure out
their chances of survival in the house?
Remember, the chance of something
happening is just how likely it is to
happen.
The probability of
something happening is
equivalent to the chance of
it happening.
1
Calculate the probability that:
a.
Brian will be evicted.
b.
Bryony will be evicted.
c.
Brad will be evicted.
d.
Bob will be evicted.
1
Calculate the probability that:
a.
Brian will be evicted.
Solution
There is only 1 Brian out of 4 possible people.
So there is a 1 in 4 chance that the person evicted will be Brian.
1
1 in 4 can be written as .
4
So the probability that Brian will be evicted is
1
4
1
Calculate the probability that:
a.
Brian will be evicted.
Solution
Probability
=
No. of favourable outcomes
No. of possible outcomes
Probability
=
No. of Brians______
No. of people up for eviction
Probability
=
1
4
(Remember: you might have to simplify fractions!)
1
a.
c.
Calculate the probability that:
Brian will be evicted.
b.
Bryony will be evicted.
1
1
4
4
Brad will be evicted.
1
4
d.
Bob will be evicted.
1
4
2
a.
Calculate the probability that the
person evicted :
Will be younger than 25.
b.
Will be female.
c.
Has exactly 3 vowels in
f.
Will be of an age that is
an odd number.
g.
Has the letter ‘b’ in their
name.
their job title.
h.
Will be Welsh.
d.
Will be Scottish.
i.
Will be older then 17.
e.
Will be younger than 23.
2
a.
b.
Calculate the probability that the
person evicted :
Will be younger than 25. 3
4
1
Will be female.
4
c.
d.
e.
f.
Will be of an age that is
g.
Has the letter ‘b’ in their
name.
3
their job title.
4
h.
Will be Welsh.
1
i.
Will be older then 17.
Will be younger than 23.
2
1
2
2
an odd number.
Has exactly 3 vowels in
Will be Scottish.
1
0
1
1
A probability scale is a method of
displaying how likely an event is to occur.
The scale goes from 0 to 1 with a probability of
• 0 meaning that the event is impossible
• 1 meaning that the event is certain
• ½ meaning that the event has an even
chance of happening
0
impossible
1
unlikely
even
likely
certain
Think about the following events and how
likely each is to occur.
a) The Sun will rise tomorrow.
b) Britney Spears will become
Prime Minister.
c) You will win the lottery.
e) You’ll have your favourite
food for dinner tonight.
f)
Roll a dice and get a 4.
g) Brian will be evicted.
d) It will rain this afternoon.
Likely?
Unlikely?
Certain?
Impossible?
Construct a probability scale showing the
chance of each event occurring. Place each
letter on the scale similar to the example
below.
(If more than one event has the same probability
write it above the other as shown.)
s
r
p
w
u
t
q
0
impossible
v
1
unlikely
even
likely
certain
Construct a probability scale showing the
chance of each event occurring. Place each
letter on the scale similar to the example
below.
a) The Sun will rise tomorrow.
b) Britney Spears will become
Prime Minister.
c) You will win the lottery.
e) You’ll have your favourite
food for dinner tonight.
f)
Roll a dice and get a 4.
g) Brian will be evicted.
d) It will rain this afternoon.
0
impossible
1
unlikely
even
likely
certain
Construct a probability scale showing the
chance of the events in Question 2 (a – i)
occurring.
Use your results for the questions you have already
answered and place each letter on the scale similar
to the example below.
(If more than one event has the same probability
write it above the other as shown.)
s
r
p
w
u
t
q
0
impossible
v
1
unlikely
even
likely
certain
A T.V. Chat Show Host asks who you
think will be the first person evicted.
Can you say for sure who will be evicted?
Why not?
The chat show host won’t give up – he really wants an
answer. You have to tell him something.
What piece of information about the evictee do you
think is most likely to be true?
1)
2)
3)
4)
He/she will be Scottish
He will be male
He/she will be younger than 23
He will be called Bob
The Chat Show Host asks why you
say this.
What do you tell him?
There’s breaking news:
The computer that selects the evictee
has contracted a virus. It cannot now
select anyone with the letter ‘o’ in their
name.
Does this change your
prediction?
120,000 people entered to become
contestants on the show.
Only a lucky 12 were randomly
selected by a computer to become
contestants.
(You might want to take a
note of these statistics!)
3
b.
a.
For each person who entered, calculate the
probability of becoming a contestant.
Assuming randomness, for each person who entered,
calculate the probability of winning.
The rules state that exactly 25% of the contestants must be Scottish.
There are no other rules concerning the nationality of contestants.
c.
How many contestants must be Scottish?
40,000 Scottish people entered to become contestants.
d. For each Scot who entered,
calculate the probability of
becoming a contestant.
e.
Assuming randomness, what is the probability that the
winner will be Scottish?
3
b.
a.
1
For each person who entered, calculate the
10, 000
probability of becoming a contestant.
Assuming randomness, for each person who entered,
calculate the probability of winning.
1
120, 000
The rules state that exactly 25% of the contestants must be Scottish.
There are no other rules concerning the nationality of contestants.
c.
How many contestants must be Scottish?
3
40,000 Scottish people entered to become contestants.
d. For each Scot who entered,
becoming a contestant.
e.
3
calculate the probability of
40, 000
Assuming randomness, what is the probability that the
1
winner will be Scottish?
4
The annoying Chat Show host is back.
He has heard rumours that Charlie’s
House of chance is fixed.
He says that a Scot had a better chance
of becoming a contestant than someone
who is not Scottish.
Is he correct?
Why/why not?
It turns out that the Chat Show Host entered to
become a contestant on Charlie’s House of Chance.
He believes that he’d have a better chance of
winning the lottery than he ever had of winning
Charlie’s House of Chance.
(Hint: the chance of winning the lottery jackpot is 1 in 14,000,000)
Is he correct?
What assumptions do you have to
make to answer that question?