2 marks 19. A certain probability course has three sections, with a total of 600 students. Section A has 300 students, Section B has 100 students and Section C has 200 students. The failure rates on the first test are: 10% for Section A, 40% for Section B and 20% for Section C. If it is known that a particular student failed the first test, what is the probability that this student is from Section B? DO NOT SIMPLIFY YOUR ANSWER.

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Problem 13. Daphne's Daisies sells two types of pots of flowers, Daisy Pot and Fern Pot. They have only enough pots to sell a total of 50 flower pots per day. There is a commitment to make at least 20 Daisy Pots and at least 10 Fern Pots every day. In addition, the shop has a profit of $6 per Daisy Pot and $4 per Fern Pot sold. If the shop makes the correct number of each type of flower pot to maximize their profit on a given day, how many of each type of flower pots will be made, and what will the profit be? A) 20 Daisy Pots and 30 Fern Pots for a profit of $240; B) 100 Daisy Pots and 10 Fern Pots for a profit of $600; C) 40 Daisy Pots and 10 Fern Pots for a profit of $280; D) 50 Daisy Pots and 0 Fern Pots for a profit of $300; E) 0 Daisy Pots and 50 Fern Pots for a profit of $200; F) none of these.

Problem 1. A flower shop makes three different types of flower arrangements: inside arrangements, wedding arrangements and garden arrangements. In a week, each inside arrangement requires 25 roses, 40 gerberas and 20 stephanotis, each wedding arrangement requires 50 roses, 10 gerberas and 25 stephanotis, and finally one garden arrangement requires 100 roses, 80 gerberas and 150 stephanotis. Each week the flower shop has 1000 roses, 850 gerberas and 2000 stephanotis to use. There is a commitment to make at most 10 inside arrangements and at least 5 wedding arrangements every week. Also, the number of the garden arrangements should not exceed the number of inside arrangements. If the profit is $15 for each inside arrangement made, $20 for each wedding arrangement and $30 for each garden arrangement made, how many arrangements of each type should the flower shop make so that will maximize their profit? A) Maximize 15.0+20y+30z subject to r < 10, y > 0,2 > 0, 25x+50y+100% <1000, 40x+10y+802 < 850, 20:r + 25y + 150z < 2000, < > 2; B) Maximize 15.0+20y+30z subject to r > 10, y > 5,2 > 0, 250+50y+1002 < 1000, 40.r+10y+802 < 850, 20:r + 25y + 150z < 2000, < > 2; C) Maximize 15x+20y+30z subject to r> 10, y >5, > 0, 25x+50y+100% <1000, 40.x+10y+80z < 850, 20:+ 25y + 150z <2000, 0, 3 < 10 y > 5, 2 > 0, 25x + 50y + 100% < 1000, 400 +10y + 802 < 850, 200 + 25y + 150z < 2000, < 0, 1 < 10, y > 5, 2 > 0, 25x + 50y + 100% < 1000, 40x + 10y + 80< 850, 20.1 + 25y + 150z < 2000, < > z; F) none of these.

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