Question

a news organization surveyed 80 adults. each said he or she gets news from only one source. here is a summary of their sources of news.
source of news number of adults
internet 21
television 23
newspaper 13
radio 23
three of the adults from the survey are selected at random, one at a time without replacement. what is the probability that none of the three adults get news from television?
do not round your intermediate computations. round your final answer to three decimal places.

Explanation:

Step1: Calculate non - TV adults

The total number of adults is 80, and the number of adults who get news from television is 23. So the number of adults who do not get news from television is $80 - 23=57$.

Step2: Calculate first - pick probability

The probability that the first - selected adult does not get news from television is $\frac{57}{80}$.

Step3: Calculate second - pick probability

Since the selection is without replacement, for the second pick, there are 79 adults left and 56 non - TV adults left. So the probability that the second - selected adult does not get news from television, given that the first one did not, is $\frac{56}{79}$.

Step4: Calculate third - pick probability

For the third pick, there are 78 adults left and 55 non - TV adults left. So the probability that the third - selected adult does not get news from television, given that the first two did not, is $\frac{55}{78}$.

Step5: Calculate overall probability

By the multiplication rule for independent events (in the context of conditional probability for non - replacement sampling), the probability that none of the three adults get news from television is $\frac{57}{80}\times\frac{56}{79}\times\frac{55}{78}=\frac{57\times56\times55}{80\times79\times78}=\frac{175560}{492960}\approx0.356$.

Answer:

0.356