Use the Shell Sort algorithm to rearrange the numbers 5, 9, 1, 7, 4, 6 into
ascending order. Explain the method, demonstrate all passes and state the
total number of comparisons and swaps. (8 marks)
Using the list of numbers, 5, 9, 1, 7, 4, 6 given in question 1,
Use the Quicksort Algorithm to rearrange the numbers into ascending
order, counting the number of comparisons and swaps. Show all steps
and explain your method. (8 marks)
A garden centre is selling a box containing 40 daffodil bulbs and 60 narcissi bulbs. The likelihood of a daffodil bulb flowering is 0.8 and 90% of the narcissi bulbs are expected to flower.
Draw a tree diagram to demonstrate these events and calculate the
probabilities of all possible outcomes of these two events. Check your
answers by summing the probabilities generated to ensure the result is 1. (3 marks)
What is the probability that a randomly chosen bulb does not flower? (2 marks)
What is the probability that a randomly chosen bulb is a narcissi
given that the bulb does not flower? (3 marks)
In a particular stretch of a river, an average of 3 shrimps have been found in a litre sample of the river water.
Use the Poisson formula to calculate . (2 marks)
Use the Poisson table to find . List the possible outcomes. (2 marks)
Calculate . (3 marks)
An online quiz has 10 questions with a choice of true or false for the answer. If someone just clicks on an answer randomly, what is the probability that:
No answers are correct? Demonstrate your answer using the formula. (2 marks)
At least seven questions are correct? Explain your calculations. (3 marks)
Less than four are correct? Explain your answer, listing outcomes. (4 marks)
The graph below shows the distance in miles between towns to be visited by a travelling salesman.
Draw the extra edges required on the graph to make it a complete
network with the weights of the extra edges corresponding to the
shortest distance between each business. (2 marks)
Use the nearest neighbour algorithm to find a tour starting and finishing
at A. Draw the tour on the complete network diagram. Explain the
algorithm and why you choose each edge. (4 marks)
List the vertices in the order they would be visited on the network above. (2 marks)
State the total weight of the tour. (2 marks)
