A company collected data on 100 people with regards to their eye color and wheth

Question

A company collected data on 100 people with regards to their eye color and whether they were left-handed or right-handed. The data is given in the table below.

(a) What is the probability that a person in this group has blue eyes?   

(b) What is the probability that a person in this group is right-handed?   

(c) What is the probability that a person in this group has blue eyes and is right-handed?   

(d) Based on the data, are having blue eyes and being right-handed independent events for this group of people?

Yes or No   

Eye Color Brown Blue Green Total Left-Handed 20    10    20    50 Right-Handed 20    15    15    50 Total 40    25    35    100

Explanation / Answer

(a) the probability that a person in this group has blue eyes= 25/100=0.25

(b) the probability that a person in this group is right-handed=50/100=0.5

(c) the probability that a person in this group has blue eyes and is right-handed=15/100=0.15

(d) Based on the data, are having blue eyes and being right-handed independent events for this group of people?

P(right handed and blue eyes)=10/100=0.15

P(right handed)=50/100=0.5

P(blue eyes)=25/100=0.25

P(right handed)*P(blue eyes)=0.5*0.25=0.125 which is not equals to P(right handed and blue eyes).

Hence both are not independent

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