Question

a drug trial had 420 participants. a survey was taken to determine how many had drowsiness as a side effect and how many had nausea 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? participants (b) how many of the participants had neither drowsiness nor nausea? participants (c) how many of the participants did not have both drowsiness and nausea? participants

Explanation:

Step1: Find participants with drowsiness

Sum parts of drowsiness - only and drowsiness - nausea overlap.
$31 + 223$

Step2: Find participants with neither

Value outside both circles.
$121$

Step3: Find participants without both

Total participants minus those with both.
$420-223$

Answer:

(a) 254 participants
(b) 121 participants
(c) 197 participants