Alan collects data about the students in his class. He records their hair color and whether they have freckles. His results are shown in the table below. Category Brown Hair Blonde Hair Red Hair Freckles 4 5 4 No Freckles 7 4 1Find each probability. P(freckles) P(blonde hair or red hair) P(freckles and brown hair) P(no freckles|red hair) (4 points)
To calculate each probability, we need to use the formula:
Probability = Number of favorable outcomes / Total number of outcomes
There are a total of 20 students in Alan's class (summing up all the numbers in the table).
1. P(freckles):
The number of students with freckles is 4 + 5 + 4 = 13.
P(freckles) = 13 / 20 = 0.65
2. P(blonde hair or red hair):
The number of students with blonde hair or red hair is 5 + 4 + 4 + 1 = 14.
P(blonde hair or red hair) = 14 / 20 = 0.7
3. P(freckles and brown hair):
The number of students with freckles and brown hair is 4.
P(freckles and brown hair) = 4 / 20 = 0.2
4. P(no freckles|red hair):
The number of students with red hair is 4 + 1 = 5.
Out of those 5 students, only 1 does not have freckles.
P(no freckles|red hair) = 1 / 5 = 0.2