MATH SOLVE

5 months ago

Q:
# The conditional relative frequency table was calculated by row using data from a survey of one station’s television programming. The survey compared the target audience with the type of show, either live or recorded, over a 24-hour time period.Which is the best description of the value 0.375 in the table?Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.Given that the program was recorded, there is a 37.5% chance that it was targeted at adults.37.5% of the programs are targeted at adults.37.5% of the programs are recorded.

Accepted Solution

A:

Answer-The correct option would be-Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.Solution-We know that, probability of A given that B is,[tex]P(A|B)=\dfrac{P(A\ \cup\ B)}{P(B)}[/tex]From the table,[tex]P(\text{Recorded})=0.417\\\\P(\text{Adult}) = 1\\\\P(\text{Recorded}\ |\ \text{Adult})=0.375[/tex]Probability that the program was recorded given that the targeted audiences were adults is,[tex]P(\text{Recorded}\ |\ \text{Adult})=\dfrac{P(\text{Recorded}\ \cup\ \text{Adult})}{P(\text{Adult})}[/tex][tex]\dfrac{0.375}{1}=0.375=37.5\%[/tex]Probability that the targeted audiences were adults given that the program was recorded is,[tex]P(\text{Adult}\ |\ \text{Recorded})=\dfrac{P(\text{Adult}\ \cup\ \text{Recorded})}{P(\text{Recorded})}[/tex][tex]\dfrac{0.375}{0.417}=0.899=89.9\%[/tex]Therefore, the first option "Given that the program was targeted at adults, there is a 37.5% chance that it was recorded." is correct