(d) Is random assignment to tents likely to ensure $\leq1~arachnophobe$ per tent?
- Random assignment and the independence assumption means that the answer to part c is the inverse of the outcome we're looking to avoid: $P(\gt1~arachnophobes) = 1-P(\leq1~arachnophobe)$. So, $P(\gt1~arachnophobes) = 1-0.84 = 0.16 = 16\%$. Those are the probabilities, but the interpretation really depends on how confident the camp counselor feels about a $16\%$ chance of having multiple arachnophobic campers in one of the tents.
+ Random assignment and the independence assumption means that the answer to part c is the complement of the outcome we're looking to avoid: $P(\gt1~arachnophobes) = 1-P(\leq1~arachnophobe)$. So, $P(\gt1~arachnophobes) = 1-0.84 = 0.16 = 16\%$. Those are the probabilities, but the interpretation really depends on how confident the camp counselor feels about a $16\%$ chance of having multiple arachnophobic campers in one of the tents.