WORKSHEET ON
THEORETICAL PROBABILITY

Problem 1 :

A die is rolled. What is the theoretical probability of getting :

a) a "six"

b) a "prime number"?

Solution

Problem 2 :

A bag contains 1 yellow, 2 green and 5 blue beds. One bead is chosen at random. Find the probability that it is :

(a)  Yellow  (b)  not yellow

Solution

Problem 3 :

1 A die numbered 1 to 6 is rolled once. Find:

a) P(3)

b) P(even number)

c) P(a number at least 1)

d) P(5)

e) P(not a 5)

f) P(a number greater than 6)

Solution

Problem 4 :

The five illustrated cards are well shuffled and placed face down on a table. One of the cards is randomly chosen. 

Solution

Problem 5 :

A bag contains 10 beads. 5 are white, 2 are red, 1 is blue, 1 is green and 1 is black. A bead is taken at random from the bag. Find:

a) P(white)

b) P(blue)

c) P(not black)             Solution

Problem 6 :

A letter is randomly chosen from GENEVA.

a)  Find the probability that it is:

(i) an E

(ii) a Z

b) Given that the letter chosen first is a G and it is removed, what is the probability that a second randomly chosen letter is a vowel?          Solution

Problem 7 :

A dart board has 30 sectors, numbered 1 to 30. A dart is thrown towards the bulls-eye and misses in a random direction. Determine the probability that the dart hits:

a) a multiple of 5

b) a number between 7 and 13 inclusive

c) a number greater than 18

d) 15

e) a multiple of 7

f) an even number that is a multiple of 3.

Solution

Answers :

(1)  (a)   1/6   (b)  1/2

(2)  (a)  1/8   (b)  7/8

(3)  (a)  1/6  (b)  1/2  (c)  1  (d)  1/6  (e)  5/6  (f)  0

(4)  (a)  2/5  (b)  1/5  (c)  4/5  (d)  4/5

(5)  (a)  1/2  (b)   1/10  (c)  9/10

(6)  (a)  (i)    1/3  (ii)  0  (b)  3/5

(7)  (a)  1/5  (b)  7/30  (c)  11/30  (d)  1/30  (e)  2/15

(f)  1/6

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