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Big Data Analytics – Homework 5

1

Question 1. [10 points] Consider a school with a total population of 100 persons. These 100

persons can be seen either as ‘Students’ and ‘Teachers’ or as a population of ‘Males’ and

‘Females’.

Female Male Total

Teacher 8 12 20

Student 32 48 80

Total 40 60 100

(a) What is the conditional probability that a certain member of the school is a ‘Teacher’ given

that he is a ‘Male’?

(b) What is the conditional probability that a certain member of the school is a ‘Teacher’ given

that she is a ‘Female’?

Question 2. [30 points] Suppose you have 1000 fruits which could be either “banana”, “orange”

or “other”. The objective is to predict if a given fruit is a “banana”, “orange” or “other” when

only the 3 features (long, sweet and yellow) are known.

Type Long Not

Long

Sweet Not

Sweet

Yellow Not

Yellow

Total

Banana 400 100 350 150 450 50 500

Orange 0 300 150 150 300 0 300

Other 100 100 150 50 50 150 200

Total 500 500 650 350 800 200 1000

(a) [6 points] Compute the prior probabilities for each of the class of fruits, i.e. ,

 

 , and    

.

(b) [15 points] Compute the probability of each of the evidences conditional on each type of

fruits.

(c) [3 points] Compute the joint probability of 3 evidences, i.e. ,   ,  .

(d) [6 points] Suppose you are given a fruit that is: Long, Sweet and Yellow, can you predict

what fruit it is?