Chapter 8.3, Problem 85E

U.S. Food and Drug Administration. An ice cream company wishes to use a new red dye to enhance the color in its strawberry ice cream. The U.S. Food and Drug Administration (FDA) requires the dye to be tested for cancer-producing potential using laboratory rats. The results of one test on $1,000$ rats are summarized in the following table

(A) Convert the table into a probability table by dividing each entry by $1,000$.

(B) Are “developing cancer” and “eating red dye” independent events?

(C) Should the FDA approve or ban the use of the dye? Explain why or why not using $P\left(C\left|R\right.\right)\text{ and }P\left(C\right).$