Question

SECTION B - ANSWER ALL QUESTIONS Question 1/20 MARKSI A) You and two friends go to a restaurant and order a sandwich. The menu has 10 types of sandwiches and each of you is equally likely to order any type. What is the probability that each of you orders a different type? [10 marks) B) The Ghanaian Diabetes Association estimates that 5.9% of Americans have diabetes. Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it. If the medical lab gives the test to a randomly selected person, what is the probability that the diagnosis is correct? [10 marks) Question 2 [20 MARKSI A) A study of major flash floods that occurred over the last 15 years indicates that the probability that a flash flood warning will be issued is 0.5 and the probability of a dam failure during the flood is 0.33. The probability of a dam failure given that a warning is issued is 0.17. Find the probability that a flash flood warning will be issued and a dam failure will occur. 15 marks] B) M&M sweets are of varying colours and the different colours occur in different proportions. The table below gives the probability that a randomly chosen M&M has each colour, but the value for tan candies is missing. Colour Brown Red Yellow Green Orange Probability 0.3 0.2 (a) What value must the missing probability be? [3 marks] (b) You draw an M&M at random from a packet. What is the probability of each of the following events? i. You get a brown one or a red one. [3 marks] ii. You don't get a yellow one. [3 marks) iii. You don't get either an orange one or a tan one. [3 marks) iv. You get one that is brown or red or yellow or green or orange or tan. [3 marks) Tan ? 0.2 0.1 0.1 Page 7 of 7

Answer 1

ution:- D. 10x10x10= 1000 Total ways to order : ways to order differently 10x9x8=720 So Plorder a different type) = 0.721 720 1000 B) D: Have diabetes T: Test positive 0.95 PD)=0.59 P15) - 0.98 PLEJE Pl Diagnoses ic correct) Plan D) + Plana P ( 5 ) . P (D) + P 11 el rey. Play 0.98 0.59 + 0.95 x 0.4) - 0.9677 9) P|W) = 0.5 D: Dam Failure W: warning issues Pleo. -0.17 P(O) = 0.33 pl Dow): P (2) .P (W) 0.17xo.5 0.085