Question

28. From the below cross classification showing the frequencies of hair and eye color of a group of staff at ABC company, and answer the following questions (a-d).

	Eye Color
Hair Color	Brown	Blue	Green	Hazel	Total
Blond	30	20	7	3	60
Brown	74	28	10	7	119
Red/Auburn	17	15	5	4	41
Black	43	11	5	1	60
Total	164	72	27	14	280

a)The probability that a staff will have blue eyes given he/she is blond.	b)The probability of black hair
c)The probability that a staff will have either red hair or green eyes.	d)The probability that a staff will have brown hair and brown eyes.

Answer 1

a) P(Blue | Blond) = 20/60 = 0.3333

The probability that a staff will have blue eyes given he/she is blond is 0.3333

b) P(Black) = 60/280 = 0.2143

The probability of black hair is 0.2143

c)

P(Red hair OR Green eyes)

= P(Red hair) + P(Green eyes) - P(Red hair AND Green eyes)

= 41/280 + 27/280 - 5/280

= 63/280

= 0.2250

The probability that a staff will have either red hair or green eyes is 0.2250

d) P(Brown hair AND Brown eyes)= 74/280 = 0.2643

The probability that a staff will have brown hair and brown eyes is 0.2643