Question

a drug trial had 662 participants. a survey was taken to determine how many had anxiety as a side effect, how many had fatigue, and how many h
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 anxiety?

participants

(b) how many of the participants had neither anxiety nor nausea?

participants

(c) how many of the participants had both fatigue and nausea, but didnt have anxiety?

participants

Explanation:

Step1: Calculate participants with anxiety

Add all sections in the anxiety circle: \(143 + 41+109 + 72\).
$$143+41 = 184$$
$$184+109 = 293$$
$$293+72 = 365$$

Step2: Calculate participants with neither anxiety nor nausea

Sum sections not in anxiety or nausea circles: \(67+53\).
$$67 + 53=120$$

Step3: Find participants with both fatigue and nausea but no anxiety

Look at the intersection of fatigue and nausea not in anxiety: \(53\).

Answer:

(a) \(365\) participants
(b) \(120\) participants
(c) \(53\) participants