Question

a drug trial had 278 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 nausea? participants (b) how many of the participants had drowsiness or nausea (or both)? participants (c) how many of the participants did not have both drowsiness and nausea? participants

Explanation:

Step1: Find the number of participants who had nausea

The number of participants who had nausea is the sum of those who had only nausea and those who had both drowsiness and nausea.
$$78 + 69$$

Step2: Find the number of participants who had drowsiness or nausea (or both)

We add the number of participants who had only drowsiness, only nausea, and both.
$$84+78 + 69$$

Step3: Find the number of participants who did not have both drowsiness and nausea

We subtract the number of participants who had both from the total number of participants. First, find the total number of participants who had drowsiness or nausea (or both) as in Step 2: $84 + 78+69=231$. Then, since the total number of participants is 278, the number of participants who did not have both is $278-78$

Answer:

(a) $147$ participants
(b) $231$ participants
(c) $200$ participants