1 . Out of 100 men, 8 are colorblind. Out of 100 women, only 1 is colorblind. Su
ID: 2921998 • Letter: 1
Question
1. Out of 100 men, 8 are colorblind. Out of 100 women, only 1 is colorblind. Suppose we randomly select one of the 200 people, and we record their gender and whether or not they are colorblind.
(a) [30 pts (12 pts for probabilities, 6 pts for terminology, 6 pts for how they compare, 6 pts for saying whether independent)]
Is being colorblind independent of gender? Answer this by comparing appropriate probabilities that you can (easily) derive from the initial information; represent these probabilities in the appropriate “P( )” notation, then say or symbolize what it is about how they compare that determines whether the events are independent. Also say whether these probabilities are joint, marginal, or conditional.
(b) [12 pts] Is there an association between gender and colorblindness? How do you know? [Hint, consider your answer to part a.]
(c) [10 pts] Produce a 2x2 joint probability table representing the information at the beginning of the exercise, and fill in all the probabilities.
(d) [6 pts (2 pts notation, 2 pts value, 2 pts terminology)]
What is the probability that someone is colorblind? Represent this probability in the appropriate “P( )” notation. Also say whether it is a joint, marginal, or conditional probability.
(e) [6 pts (2 pts notation, 2 pts value, 2 pts terminology)]
What is the probability that someone selected from the whole group is a colorblind male? Represent this probability in the appropriate “P( )” notation. Also say whether it is a joint, marginal, or conditional probability.
(f) [4 pts] Verify your answer from (a) regarding independence by comparing your answer in (e) to some other value (show any calculation you perform); say or symbolize what it is about how they compare that determines whether the events are independent.
(g) [4 pts] Suppose we randomly encounter someone who is colorblind. What is the probability this person is male? Represent this in appropriate probability P( ) notation, then give the value. Show any calculation.
Explanation / Answer
(a) Is being colorblind independent of gender? Answer this by comparing appropriate probabilities that you can (easily) derive from the initial information; represent these probabilities in the appropriate “P( )” notation, then say or symbolize what it is about how they compare that determines whether the events are independent. Also say whether these probabilities are joint, marginal, or conditional.
Answer; Proportion of Female colourblind = pfemale = 1/100 = 0.01
Proportion of male colourblind = pmale = 8/100 = 0.08
For independence.
As P(Male and Colorblind) = P(Male) * P(Color blind)
P(Male and Colorblind) = 8/200 = 0.04
P(Male) = 0.5 and P(color blind) = 9/200 = 0.045
so both male and colorblindness are not independent. SMilarly, events " females" and " color blindness" are not indpeendent.As, these events are Conditional Distribution.
(b) Is there an association between gender and colorblindness? How do you know?
Answer : Yes, There is an association between gender and colorblindness and i come to know as we see that these events are not independent in nature.
(c) Produce a 2x2 joint probability table representing the information at the beginning of the exercise, and fill in all the probabilities.
Answer: The 2x2 joint probability table
(d) What is the probability that someone is colorblind? Represent this probability in the appropriate “P( )” notation. Also say whether it is a joint, marginal, or conditional probability.
Anser: Pr( Someone is colorblind) Pcolorblind= (8+1)/ (100+ 100) = 9/200 = 0.045
The given probability is joint probability.
(e) What is the probability that someone selected from the whole group is a colorblind male? Represent this probability in the appropriate “P( )” notation. Also say whether it is a joint, marginal, or conditional probability.
Answer: Pr( Colorblind male) =8/ (100 + 100) = 0.04
The given distribution is Marginal probability.
(f) Verify your answer from (a) regarding independence by comparing your answer in (e) to some other value (show any calculation you perform); say or symbolize what it is about how they compare that determines whether the events are independent.
Answer :
As P(Male and Colorblind) = P(Male) * P(Color blind)
P(Male and Colorblind) = 8/200 = 0.04
P(Male) = 0.5 and P(color blind) = 9/200 = 0.045
so both male and colorblindness are not independent.
(g) Suppose we randomly encounter someone who is colorblind. What is the probability this person is male? Represent this in appropriate probability P( ) notation, then give the value. Show any calculation.
Pr (Male l Colorblind) = 8/ (8 + 1) = 8/9 - 0.8889
Colorblind/ Gender Male Female Yes 0.04 0.005 No 0.46 0.495Related Questions
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