alan collects data about the students in his class. he records their hair color and whether they have have freckles. his results are shown in the table below.
find each probability
a. P(freckles)
b. P(blonde hair or red hair)
c. P(freckles and brown hair)
d. P(no freckles | red hair)
To calculate the probabilities, we need to use the given data in the table:
Hair Color | Freckles
---------------------
Blonde | Yes
Brown | No
Red | Yes
Brown | Yes
Blonde | No
a. P(freckles) = Number of students with freckles / Total number of students
We can see that there are 2 students with freckles, so the numerator is 2. The total number of students is 5 since there are 5 rows in the table. Therefore, the denominator is 5.
P(freckles) = 2/5 = 0.4
b. P(blonde hair or red hair) = Number of students with blonde hair or red hair / Total number of students
There are 2 students with blonde hair and 1 student with red hair. So, the numerator is 2 + 1 = 3. The total number of students is still 5.
P(blonde hair or red hair) = 3/5 = 0.6
c. P(freckles and brown hair) = Number of students with freckles and brown hair / Total number of students
From the table, we can see that there is only 1 student with freckles and brown hair. The total number of students remains 5.
P(freckles and brown hair) = 1/5 = 0.2
d. P(no freckles | red hair) = Number of students with no freckles and red hair / Number of students with red hair
We see that there are no students with red hair and no freckles. Therefore, the numerator is 0. The denominator is the number of students with red hair, which is 1.
P(no freckles | red hair) = 0/1 = 0