P (sum> 10) = 3/36
= 0.08333
= 0.08333 x 100
= 8.33%
ii) What is the probability that the number on the red die is one larger than the
number on the blue die?
P ( number on red die is one larger than the blue die) = 5/36
= 0.138
= 0.138 x 100
= 13.8 %
iii) What is the probability that the sum of the two numbers is less than 11?
P ( sum< 11) = 33/36
= 0.916
= 0.916 x 100
= 91.6%
4

5 )
Use a tree diagram to explain why the probability that a family with four
children all have the same gender is 1/8
. Assume that the probability of
having a girl is equal to the probability of having a boy.
The first line represent child #1. The second line tells us that there are 4 ways to
have 2 children 2 x 2 = 4. Line 3 gives us 8 different ways to have 3 kids 2 x 4 = 8.
The fourth line gives us 16 different ways to have 4 children 2 x 8 = 16.
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?
24C2 = 276 ways of selecting 2 books from 24 books.
3 ways of choosing books of different kind
Novel + biography
Novel + war history
Biography + history war
Each pair is 8 x 8 = 64
Therefore total is 3 x 64 = 192
P ( two books are of different types) = 192/276 = 16/23
7) The probability that Prasha will score above a 90 on a mathematics test is
4/5 . What is the probability that she will score above a 90 on exactly 3 of the 4
tests this quarter?
P( Prasha scores above 90 on 3 of the 4 tests) = nCr(p)^r(q)^n-r
n= 4
r=3 p=
⅘
q=
⅕
= 4C3(
⅘
)^3(
⅕
)^4-3
5

= 4(0.512)(
⅕
)
= 226/620 = 113/310
Therefore, the probability that she will score above 90 on exactly 3 of the 4 tests is
113/310
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.

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- Spring '19
- Probability theory, Hypergeometric Distribution, Maya Dras