A survey finds that 38% of kids like tv, 24% like radio, and 13% like both.
A.Find percent of kids that like tv but not radio.
B.Find the percent of kids that like neither tv or radio.
C.Find the percent of kids like either tv or radio
D.Find the conditional probability that a kid likes radio given that heshe likes tv.
To solve this problem, we will need to use set theory and basic probability calculations. Let's go through each question step by step:
A. Find the percent of kids that like TV but not radio.
To find this, we need to subtract the percentage of kids who like both TV and radio from the percentage of kids who like TV.
First, find the percentage of kids who like TV only:
Percentage of kids who like TV only = Percentage of kids who like TV - Percentage of kids who like both TV and radio
Percentage of kids who like TV only = 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 this, we need to subtract the percentage of kids who like either TV or radio from 100% (since the total percentage should add up to 100%).
Percentage of kids who like neither TV nor radio = 100% - (Percentage of kids who like TV + Percentage of kids who like radio - Percentage of kids who like both TV and radio)
Percentage of kids who 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 who like either TV or radio.
To find this, we need to add the percentages of kids who like TV and radio and then subtract the percentage of kids who like both.
Percentage of kids who like either TV or radio = Percentage of kids who like TV + Percentage of kids who like radio - Percentage of kids who like both TV and radio
Percentage of kids who 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.
The conditional probability can be calculated using the formula:
Conditional probability = (Probability of both events occurring) / (Probability of the given event)
In this case, the probability of both events occurring is the percentage of kids who like both TV and radio, which is 13%. The probability of the given event (liking TV) is 38%.
Conditional probability = 13% / 38% = 0.3421 (rounded to four decimal places)
Therefore, the conditional probability that a kid likes radio given that he/she likes TV is approximately 0.3421.