To find each probability, we will use the following formulas:
A. P(freckles) = (Number of students with freckles) / (Total number of students)
B. P(blonde hair or red hair) = (Number of students with blonde hair or red hair) / (Total number of students)
C. P(freckles and brown hair) = (Number of students with freckles and brown hair) / (Total number of students)
D. P(no freckles|red hair) = (Number of students with no freckles and red hair) / (Number of students with red hair)
Given that the table is as follows:
Brown Hair Blonde Hair Red Hair
Freckles 4 5 4
No Freckles 7 4 1
We can calculate the probabilities:
A. P(freckles) = (4 + 5 + 4) / (4 + 5 + 4 + 7 + 4 + 1) = 13 / 25 = 0.52
B. P(blonde hair or red hair) = (5 + 4 + 4) / (4 + 5 + 4 + 7 + 4 + 1) = 13 / 25 = 0.52
C. P(freckles and brown hair) = 4 / (4 + 5 + 4 + 7 + 4 + 1) = 4 / 25 = 0.16
D. P(no freckles|red hair) = 1 / (4 + 1) = 1 / 5 = 0.2