A survey of 815 students is asked whether or not they have cable TV and Internet cable in their rooms at home.
Results of the survey showed that 69% of students has cable TV, 58% of students has Internet cable and 37% of students has both cable TV and Internet cable.
Suppose, one student is chosen randomly. Given that the student has Internet cable, what is the probability that he or she does not have cable TV ?
To find the probability that a randomly chosen student with Internet cable does not have cable TV, we can use conditional probability.
Let's first calculate the probability that a student has both cable TV and Internet cable. According to the survey, 37% of students have both. So, the probability of a student having both cable TV and Internet cable is 37/100 or 0.37.
Next, we need to calculate the probability that a student has only Internet cable. This can be done by subtracting the probability of having both from the probability of having just Internet cable.
Since 58% of students have Internet cable, and 37% have both, the probability of having only Internet cable is 58% - 37% = 21%.
Now, we can find the probability that a student with Internet cable does not have cable TV. This is the probability of having only Internet cable divided by the probability of having Internet cable:
Probability (not having cable TV | having Internet cable) = Probability (having only Internet cable) / Probability (having Internet cable)
Probability (not having cable TV | having Internet cable) = 21% / 58%
Probability (not having cable TV | having Internet cable) = 0.21 / 0.58
Probability (not having cable TV | having Internet cable) ≈ 0.3621 or 36.21%
Therefore, the probability that a student with Internet cable does not have cable TV is approximately 36.21%.