Medical case histories indicate the different illnesses may produce identical symptoms. Suppose a particular set of symptoms, which we will denote as event H, occurs only when any

of three illnesses A, B or C occurs. (Assume and ) are mutually exclusive. Studies show these probabilities of getting the

three illnesses

P A^ ^ h h = 0.01, P B = 0.005, P C^ h = 0.02.

The probabilities of developing the symptoms H, given a specific illness are

P H( | A) 0 = .9, ( P H | ) B P = 0.95, ( | H C) 0 = .75.

Assuming that an ill person shows symptoms H. Find the

probability that the person has illness A. i.e. find P A_ i | H

2 A space of elementary events S can be divided into two

events E1

, E2 that occur with probabilities 60% and 40%

respectively. An event A occurs 30% of the time in the

first event E1 and 50% of the time in the second event E2

.

What is the unconditional probability of the event A, regardless of which event it comes from.

3 There are two boxes, the first one contains 4 white balls, and

6 black balls and the second one contains 8 white balls and 3

black balls. If we choose one box at random and take a ball

from it randomly, find the probability that:

a The chosen ball is black.

b If the chosen ball was black find the probability of getting

it from the first box.

4 A factory has three machines I, II, III. If machine I produces

20% of the items, machine II produces 30%, and machine III

produces 50% of the items, with defective from the machine as

5%, 2% and 1% respectively. If an item is selected at random,

find the probability that the item is not defective.

5 A manufacturer makes two models of an item, model I, which

accounts for 80% of units sales and model II, which accounts

for 20% of units sales. Because of defects, the manufacturer

has to replace 10% of its model I and 18% of its modelII. If a

model is selected at random. Find the probability that it will

be defective

Joe drives a car at 120 mph for the half of the journey and 140 mph for the second half. What's his average speed? which mean you will use HM,GM or AM? Select one: O a. Artimatic mean (H): 129.2307mph O b. Arithematic mean (A): 129.2307 mph c. Harmonic mean (H): 129.2307 mph O d. Harmonic Mean:130mphQ2) Points obtained (... ) A horizontal distance (CD) was measured in two groups of observations where the measured distances of group "A" has the given weights as 1, 2, 9, 4 respectively and the measured distances of group "B" of equal weights. Compute the following:.... (.../10) No. Observer A Measured distance (m) 479.418 2 479.319 3 479.78 4 479.201 No. Observer B Measured distance (m) 1 478.842 2 478.706 3 479.515 4 479.253 5 479.114 The arithematic mean for each group? ii) The most probable value of the measured distance (CD)?Q 1) show that in frequency distribution ( xifi) ; i = 1,2.. n mathematical expectation of the random variable is nothing but its arithematic mean. 2) If the events A and B are Independent of A and B Separately, is it necessary that they are independent of AnB ? Justify