A survey is done to prove effects of a medication on 100 children of different r

Question

A survey is done to prove effects of a medication on 100 children of different races. There are 2 levels of effects(Positive or Negative) and 2 types of races Asian and African. Asian and Positive = 20, Asian and negatives 10 African and Positive =30, African and Negative-40 The 2X2 table is given below. Effect Positive Negative Asian 20 African 30 Let A=Negative effect 10 Race 40 B= African Race 1. Find the probability of getting positive effect. 2. Find the probability of getting an Asian race and negative effect 3. Find the probability of getting a negative effect or an African race? 4. Given a child is an African, find the probability of getting a negative effect? 5. Is being an African child independent of having a negative effect? Why?

Explanation / Answer

Ans:

1)P(positive effect)=P(Asian and positive)+P(african and positive)

=(20+30)/100=50/100=0.5

2)P(Asian and negative)=10/100=0.1

3)P(negative effect or african race)=P(negative effect)+P(african race)-P(negative and african)

=(10+40)/100+(30+40)/100-40/100

=(10+40+30+40-40)/100=80/100=0.8

4)P(negative effect/african)=P(negative and african)/P(african)=(40/100)/(70/100)=4/7=0.5714

5)P(african and negative)=40/100=0.4

P(african)*P(negative)=(70/100)*(50/100)=0.35

As,P(african and negative) is not equal to P(african)*P(negative),hence both events are not independent.

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