August 2000
MA214 : DISCRETE MATHEMATICS

QUESTION 2

Total Marks: 15 Marks

• Question 1
• Question 3
• Question 4
• Question 5
• Cover Page

SUGGESTED SOLUTIONS
Solutions and allocated marks are indicated in green.
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(a) A bit string of length 10 is chosen at random.
(i) How many such bit strings are there? [2]
(ii) In how many different ways can the bit string contain exactly three 0’s? [2]
(iii) In how many different ways can the bit string be chosen so that the first
five bits contain exactly three 0’s and the last five bits contain exactly
two 0’s? [3]
(iv) In how many different ways can the bit string contain at least two 0’s? [3]

(b) Let A and B be two events. You are given the following probabilities:
P(A)=0.7 P(B)=0.5 P(AB) = 0.8
Are the events A and B independent? Justify your answer. [5]

Do not award any marks for stating that the events are not
independent unless the candidate justifies his or her answer.