Question
Mia surveyed the students at her school to find out if they like the color black and/or pink. The results of her survey are shown in the two-way table below:
Like Black
Do Not Like Black
Total
Like Pink
27
41
68
Do Not Like Pink
23
9
32
Total
50
50
100
If a student does not like pink, what is the probability that student also does not like black? (5 points)
Like Black
Do Not Like Black
Total
Like Pink
27
41
68
Do Not Like Pink
23
9
32
Total
50
50
100
If a student does not like pink, what is the probability that student also does not like black? (5 points)
Answers
GPT 3.5
The probability that a student does not like black given that they do not like pink can be calculated using the formula for conditional probability:
P(Do not like black | Do not like pink) = number of students who do not like black and do not like pink / number of students who do not like pink
From the table, we can see that there are 9 students who do not like black and do not like pink. The total number of students who do not like pink is 32.
So, the probability that a student does not like black given that they do not like pink is:
P(Do not like black | Do not like pink) = 9/32
P(Do not like black | Do not like pink) = 0.28125
Therefore, the probability that a student does not like black given that they do not like pink is 0.28125 or approximately 28.13%.
P(Do not like black | Do not like pink) = number of students who do not like black and do not like pink / number of students who do not like pink
From the table, we can see that there are 9 students who do not like black and do not like pink. The total number of students who do not like pink is 32.
So, the probability that a student does not like black given that they do not like pink is:
P(Do not like black | Do not like pink) = 9/32
P(Do not like black | Do not like pink) = 0.28125
Therefore, the probability that a student does not like black given that they do not like pink is 0.28125 or approximately 28.13%.