Question

a drug trial had 288 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 venn diagram: two circles, left labeled \had drowsiness\ with 44, intersection 101, right labeled \had nausea\ with 41, outside the circles 102 (a) how many of the participants had drowsiness? \boxed{} participants (b) how many of the participants had neither drowsiness nor nausea? \boxed{} participants (c) how many of the participants did not have both drowsiness and nausea? \boxed{} participants

Explanation:

Part (a)

Step1: Identify drowsiness groups

The drowsiness circle has two parts: only drowsiness (44) and both drowsiness and nausea (101).

Step2: Sum the two parts

To find the total with drowsiness, add these two numbers: $44 + 101 = 145$.

Step1: Find total with side effects

First, find the total number of participants with either drowsiness, nausea, or both. Add the three parts of the Venn diagram: $44 + 101 + 41 = 186$.

Step2: Subtract from total participants

Total participants are 288. Subtract the number with side effects to find those with neither: $288 - 186 = 102$. Wait, but the diagram shows 102 outside? Wait, no, wait: Wait, the Venn diagram's outside is 102? Wait, no, let's re - check. Wait, the Venn diagram has: only drowsiness (44), both (101), only nausea (41), and outside (102)? Wait, no, the total of the three regions (44 + 101+41) is 186. Then 288 - 186 = 102. So the number with neither is 102.

Step1: Find number with both

The number of participants with both drowsiness and nausea is 101 (from the overlapping region).

Step2: Subtract from total

To find the number without both, subtract the number with both from the total number of participants: $288 - 101 = 187$.

Answer:

145

Part (b)