please show all work (4) The following table summarizes the hair and eye color o

Question

please show all work

(4) The following table summarizes the hair and eye color of a small statistics class at ESCC during the Spring 2016 semester Eye Color Blue Green Brown Black | Total Blonde Red Brown Black 2 2 Total 10 25 One student is selected at random. Determine the following probabilities: (a) P(student has blue eyes, given that the student has black hair) (b) P(student has black hair, given that the student has blue eyes) (c) P(student has blue eyes OR black hair) (d) P(student red hair AND brown eyes)

Explanation / Answer

Ans:

a)P(blue eyes/black hair)=P(blue eyes and black hair)/P(black hair)

=(1/25)/(6/25)=1/6

b)P(black hair/blue eyes)=P(black har and blue eyes)/P(blue eyes)=(1/25)/(5/25)=1/5

c)P(blue eyes or black hair)=P(blue eyes)+P(black hair)-P(blue eyes and black hair)

=(5/25)+(6/25)-(1/25)=(5+6-1)/25=10/25

d)P(red hair and brown eyes)=2/25

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