To solve these percentage problems, we need to use set theory and basic math operations. Let's break down each question one by one:
A. Find the percent of kids that like TV but not radio:
To find the percent of kids that like TV but not radio, we need to subtract the percentage of kids that like both TV and radio from the percentage of kids that like TV.
Percentage of kids that like TV but not radio = Percentage of kids that like TV - Percentage of kids that like both TV and radio.
Given that 38% of kids like TV and 13% like both TV and radio:
Percentage of kids that like TV but not radio = 38% - 13% = 25%.
Therefore, 25% of kids like TV but not radio.
B. Find the percent of kids that like neither TV nor radio:
To find the percent of kids that like neither TV nor radio, we need to subtract the sum of the percentage of kids that like TV, the percentage of kids that like radio, and the percentage of kids that like both TV and radio from 100%.
Percentage of kids that like neither TV nor radio = 100% - (Percentage of kids that like TV + Percentage of kids that like radio - Percentage of kids that like both TV and radio).
Given that 38% of kids like TV, 24% like radio, and 13% like both TV and radio:
Percentage of kids that like neither TV nor radio = 100% - (38% + 24% - 13%) = 100% - 49% = 51%.
Therefore, 51% of kids like neither TV nor radio.
C. Find the percent of kids that like either TV or radio:
To find the percent of kids that like either TV or radio, we need to add the percentage of kids that like TV, the percentage of kids that like radio, and then subtract the percentage of kids that like both TV and radio.
Percentage of kids that like either TV or radio = Percentage of kids that like TV + Percentage of kids that like radio - Percentage of kids that like both TV and radio.
Given that 38% of kids like TV, 24% like radio, and 13% like both TV and radio:
Percentage of kids that like either TV or radio = 38% + 24% - 13% = 49%.
Therefore, 49% of kids like either TV or radio.
D. Find the conditional probability that a kid likes radio given that he/she likes TV:
To find the conditional probability that a kid likes radio given that he/she likes TV, we need to calculate the percentage of kids that like both TV and radio divided by the percentage of kids that like TV.
Conditional probability that a kid likes radio given that he/she likes TV = Percentage of kids that like both TV and radio / Percentage of kids that like TV.
Given that 38% of kids like TV and 13% like both TV and radio:
Conditional probability that a kid likes radio given that he/she likes TV = 13% / 38% = 34.21%.
Therefore, the conditional probability that a kid likes radio given that he/she likes TV is approximately 34.21%.