Red die
Blue die
1
2
3
4
5
6
1
1
,
1
1,
2
1,
3
1,
3
1,
5
1,
6
2
2
,
1
2
,
2
2
,
3
2
,
4
2
,
5
2
,
6
3
3
,
1
3
,
2
3
,
3
3
,
4
3
,
5
3
,
6
4
4
,
1
4
,
2
4
,
3
4
,
4
4
,
5
4
,
6
5
5
,
1
5
,
2
5
,
3
5
,
4
5
,
5
5
,
6
6
6
,
1
6
,
2
6
,
3
6
,
4
6
,
5
6
,
6
P (red 1 larger than blue) = 5/36
P (red 1 larger than blue) = 0.138
P (red 1 larger than blue) = 0.138 x 100
P (red 1 larger than blue) = 13.8%

Therefore the probability of the number on the red die being one larger than the number on the blue die
is 1/12 in a fraction, 0.138 in a decimal, or 13.8%.
iii.
What is the probability that the sum of the two numbers is less than 11?
Red die
Blue die
1
2
3
4
5
6
1
1
,
1
1,
2
1,
3
1,
3
1,
5
1,
6
2
2
,
1
2
,
2
2
,
3
2
,
4
2
,
5
2
,
6
3
3
,
1
3
,
2
3
,
3
3
,
4
3
,
5
3
,
6
4
4
,
1
4
,
2
4
,
3
4
,
4
4
,
5
4
,
6
5
5
,
1
5
,
2
5
,
3
5
,
4
5
,
5
5
,
6
6
6
,
1
6
,
2
6
,
3
6
,
4
6
,
5
6
,
6
P (sum <11) = 33/36
P (sum <11) = 11/12
P (sum <11) = 0.916
P (sum <11) = 0.916 x 100
P (sum <11) = 91.6%
Therefore the probability that the sum of the two numbers is less than 11 is 11/12 in a fraction, 0.916 in a
decimal, or 91.6%.
8 marks

5.
Use a tree diagram to explain why the probability that a family with four children all have the
same gender is
. Assume that the probability of having a girl is equal to the probability of having
a boy.
6.
In a library box, there are 8 novels, 8 biographies and 8 war history books.
If Jack selects two books at random, what is the probability that the two books are of different types?
There is a total of 24 books

There are 3 ways to choose two different types of books:
(novel + biography), (biography + war), (novel + war)
Since there are 8 novels of each type and 3 ways to pick 2 different types, do the equation
(8 x 8) x 3 = 192
To choose 2 from 24 books do the equation:
24C2 = 276
P (two different types) =192/276
P (two different types0 = 16/23
Therefore the probability of selecting 2 different types of books is 16/23 or 0.6957.
3 marks
7.
The probability that Prasha will score above a 90 on a mathematics test is 4/5 (0.8). What is the
probability that she will score above a 90 on exactly 3 of the 4 tests this quarter?
P (3) =
4
C
3
x 0.8
(3)
x
(0.2)
1
P (3) = 256/625
P (3) = 0.4096
Therefore the probability that Prasha will score above 90 on exactly 3 of her 4 math tests this quarter
is 0.4096.
4 marks
8.
A company manufacturing laptops believes that 5% of their computers are faulty. They take a
sample of 30 computers. Showing your calculations, find the probability that;
a.
Two of the laptops are faulty.
P (2) =
30
C
2
x 0.05
2
x (1-0.05)
28
P (2) =
30
C
2
x 0.05
2
x 0.95)
28
P (2) = 0.2586
Therefore the probability that two of the laptops are faulty is 0.2586
b.
More than two of the laptops are faulty.
First, I need to calculate the probabilities of having 3-30 faulty laptops. I did this through excel as shown
here:

Next, I need to add the sums of the probability of having 3-30 faulty laptops.
The sum of P (3-30) = 0.12705

Therefore the probability of having more than two faulty laptops is 0.121705.
4 marks
9.
There are six cats and seven dogs in the local animal shelter. Four animals are chosen at random to
visit a local school to educate the children on the great need for homes for these animals.

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- Fall '19
- Probability theory, Binomial distribution, Hypergeometric Distribution