Question

a drug trial had 360 participants. a survey was taken to determine how many had drowsiness as a side effect and how many had anxiety as a side effect. the venn diagram below shows the results. (each number gives the number of participants who fall into that venn diagram category.) (a) how many of the participants had drowsiness? (b) how many of the participants had neither drowsiness nor anxiety? (c) how many of the participants did not have both drowsiness and anxiety?

Explanation:

Step1: Find number of participants with drowsiness

Add participants with only drowsiness and those with both drowsiness and anxiety. So, \(107 + 86=193\).

Step2: Find number of participants with neither drowsiness nor anxiety

The number outside the two - circles in the Venn - diagram represents this group, which is 68.

Step3: Find number of participants without both drowsiness and anxiety

Subtract the number of participants with both drowsiness and anxiety from the total number of participants. Total participants are \(360\), and those with both are \(86\). So, \(360−86 = 274\).

Answer:

(a) 193 participants
(b) 68 participants
(c) 274 participants