Question

a drug trial had 210 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.) all participants in the survey
(a) how many of the participants had drowsiness?
(b) how many of the participants had neither drowsiness nor nausea?
(c) how many of the participants did not have both drowsiness and nausea?

Explanation:

Step1: Calculate the number of participants with drowsiness

To find the number of participants with drowsiness, we add the number of participants who had only drowsiness and those who had both drowsiness and nausea.
$$26 + 87=113$$

Step2: Calculate the number of participants with neither drowsiness nor nausea

We use the total number of participants and subtract the sum of participants in all the non - neither regions. The sum of participants in the drowsiness and nausea regions is \(26 + 87+49\). The total number of participants is \(210\).
$$210-(26 + 87+49)=210 - 162=48$$

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

We use the total number of participants and subtract the number of participants who had both drowsiness and nausea.
$$210 - 87=123$$

Answer:

(a) \(113\) participants had drowsiness.
(b) \(48\) participants had neither drowsiness nor nausea.
(c) \(123\) participants did not have both drowsiness and nausea.