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Probability with Permutation and Combination. :)

Total questions: 20

Worksheet time: 5hrs 0mins

Name
Class
Date
1.

There are 10 students in a class: 5 boys and 5 girls.

If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a girl?

a)

1/12

b)

1/2

c)

1

d)

1/5

2.
If three alphabets are to be chosen from A, B, C, D and E such that repetition is not allowed then what is the probability of randomly guessing the password?
a)
1/60
b)
1/45
c)
1/200
d)
1/175
3.

There are 10 men and 6 women working at a company. A hiring committee of 4 staff members is selected by a supervisor.

What is the probability that the committee is made up of 3 women and 1 man?

a)

10/91

b)

1/20

c)

3/16

d)

36/91

4.

There are 10 men and 6 women working at a company. A hiring committee of 4 staff members is selected by a supervisor.

How many ways can the committee be made up of 3 women and 1 man?

a)

200

b)

180

c)

560

d)

1820

5.

You are dealt 5 cards from a standard deck of playing cards. What is the probability you are dealt a flush?


**A flush is all 5 cards of the same suit (order does not matter).

a)

1/1287

b)

1/2598960

c)

1287/2598960

d)

5/52

6.

Probability of Empty set is

a)

0

b)

1

c)

2

d)

3

7.

Set is a well defined collection of objects

a)

True

b)

False

8.

Permutation is the ......................

a)

Selection of objects

b)

Arrangement of Objects

c)

Arrangement -selection of objects

d)

None of these

9.

The numerical measure of uncertainty is provided by .....

a)

Theory of Probability

b)

Theory of Excel

c)

Theory of Python

d)

Theory of C-language

10.
Combination is the situation when
a)
A different result occurs when positions of objects are switched
b)
The same result occurs when positions of objects are switched
c)
counting principles are applied
d)
I don't know
11.
Permutation is the situation when
a)
A different result occurs when positions of objects are switched
b)
The same result occurs when positions of objects are switched
c)
counting principles are applied
d)
I don't know
12.
When do we use the formula "nPr"?
a)
Permutation. All objects distinct
b)
Permutation. Some identical objects
c)
Arranging people in a row
d)
Forming a group of r objects
13.
When do we use the formula "n!/(a!*b!*...)"?
a)
Permutation. All objects distinct
b)
Permutation. Some identical objects
c)
Arranging people in a row
d)
Forming a group of r objects
14.

A software engineer creates a LAN game where an 8 digit code made up of 1,2,3,4,5,6,7,8 has to be decided on as a universal code. There is a condition that each number has to be used and no number can be repeated. What is the probability that first 4 digits of the code are even number?

a)

1/70

b)

1/840

c)

1/8

d)

1/40320

15.

A bag has 3 red marbles, 2 blue and 4 green and 1 yellow. What is the theoretical probability of pulling a red?

a)

3/10

b)

3/9

c)

1/9

d)

1/3

16.
You have 15 milk chocolate Valentines and 10 dark chocolate Valentines.  What is the probability that the first Valentine handed out is milk chocolate and the second is dark chocolate.
a)
¼
b)
½
c)
d)
17.
Jim draws 4 cards from a deck of cards.  What is the probability of all 4 cards being clubs?
a)
13C4
52P4
b)
13C4
52C4
c)
1
52C4
d)
1
52P4
18.
Eight racers are running and Tom wants to know his probability to earn a medal (Gold, Silver or Bronze).
a)
b)
c)
d)
19.
12C3
a)
0
b)
1
c)
220
d)
1140
20.
Find the theoretical probability of NOT landing on yellow if you spin the spinner.
a)
1/8
b)
7/8
c)
1
d)
7