Transcript Probability - s3.amazonaws.com

Probability
True or False?
Answers
A
When you roll a fair sixsided dice, it is harder to roll
a six than a four.
False – a fair
dice, so all
numbers have
equal chance
B
Scoring a total of three with
two dice is twice as likely as
scoring a total of two.
True – look at the
combinations:
next slide
True – look at the combinations:
A score of two can only be obtained
in one way – a 1 on each dice.
A score of three can be obtained in
two ways – 1 and 2 or 2 and 1, so
the three is twice as likely.
C
In a lottery, the six numbers
3, 12, 26, 37, 44, 45 are more
likely to come up than the six
numbers 1,2,3,4,5,6.
False – each
number has the
same chance
D
When two coins are tossed
there are three possible
outcomes: two heads, one head,
or no heads.
The probability of two heads is
therefore 1 False – look at the
3
combinations:
next slide
False because
there are four
outcomes:
HH, HT, TH, TT
So the probability
of HH is one out
of four, or
1
4
E
There are three outcomes in a
football match: win, lose or
draw.
The probability of winning, if
the teams are equally matched,
is therefore 1
3
False, and I have tried to explain
why...(next slide)
Suppose team A score 1 goal, and team
B scores other possible numbers:
A, B
1, 0
1, 1
1, 2
1, 3
1, 4 etc
Only one of these results is a draw, the
rest are all win or lose, so the draw is
least likely. Check some football scores
on a Saturday, it is FALSE
F
In a ‘true or false’ quiz with
ten questions, you are certain
to get five right if you just
guess.

False – you would expect five right, but
because of chance it won’t happen
every time.
G
After tossing a coin and
getting a head five times in a
row, the next toss is more
likely to be a tail than a
head.
False – only gamblers believe their luck
will change. The probability will be 1/2
each time, whatever happened before.
H
In a group of ten people the
probability of two people
being born on the same day
of the week is 1.
True. There are only
seven days in a week,
so some pair must have
been born on the same
day.
I
My friend has four
daughters. If she has
another baby, it is more likely
to be a girl than a boy.
False, same as with the coin, unless
you look at scientific results, which
might suggest various things.
J
The probability of getting
exactly three heads when I
toss a coin six times is ½.
False – and there are a
large number of
possible outcomes.
The actual probabilities are
shown on the next page.
Number of heads
The
calculations
are based on
something
called the
Binomial
Distribution
Probability
0
0.015625
1
0.093750
2
0.234375
3
0.312500
4
0.234375
5
0.093750
6
0.015625
K
There is an evens
chance of it raining
on any given day.
False – just look at any weather
records. It really does not rain on half
the days of a year.
L
It is harder
to score a
double than
any other
combination
of dice.
True – see the next slide
Imagine two separate dice, one red and one blue. The
combinations are as follows:
Red
Dice
1
2
3
4
5
6
1
1, 1
2, 1
3, 1
4, 1
5, 1
6, 1
2
1, 2
2, 2
3, 2
4, 2
5, 2
6, 2
Blue
3
1, 3
2, 3
3, 3
4, 3
5, 3
6, 3
Dice
4
1, 4
2, 4
3, 4
4, 4
5, 4
6, 4
5
1, 5
2, 5
3, 5
4, 5
5, 5
6, 5
Of the thirty six combinations, only six are doubles,
which is not half of all possible results.
6
1, 6
2, 6
3, 6
4, 6
5, 6
6, 6
False – see the
next page.
M
Coming into college I could
be early, on time, or late.
Therefore the probability
of being late is 1/3.
Look at past records. I haven’t
been late this year, so the
probability is zero.
Actually, over a college year, there
is a small probability that I just
might be late!
N
The probability of there being
an eclipse at noon tomorrow is
zero.
True – again,
look at the
records.
O
If I play the national
lottery, I have just as much
chance of winning as anyone
else.
False – some people
may buy lots more
tickets than you.
How did you fare?
Colin