Lactose intolerance causes difficulty digesting dairy products that contain lactose (milk sugar). It is particularly common among people of African or Asian ancestry. At a college, 70% of the population is white; 20% is black; and 10% is Asian. Moreover, 15% of whites, 70% of blacks, and 90% of Asians are lactose intolerant. Consider the (partially) completed tree diagram below:
Probability
.595
0.85
Tolerant
White
0.15
Lactose Intolerant
0.70
(a)
(c)
Tolerant
Black
(d)
Lactose Intolerant
(b)
(e)
Tolerant
Asian
(f)
Lactose Intolerant
The probability that a random chosen student (regardless of race) is lactose intolerant is
0.105
0.140
0.090
0.335