As part of a drug trial, a survey was done to gather information about the participants' experiences with side effects. Here are the results.

•689 people participated in the drug trial in all

• 271 of the participants had dizziness

• 86 of the participants had both dizziness and fatigue, but didn't have anxiety

• 23 of the participants had both dizziness and anxiety, but didn't have fatigue

• 93 of the participants had fatigue, but had neither dizziness nor anxiety

• 62 of the participants had anxiety, but had neither dizziness nor fatigue

• 36 of the participants had dizziness, but had neither anxiety nor fatigue

•585 of the participants had at least one of these three side effects (dizziness, anxiety, fatigue)

Construct a Venn diagram illustrating these results. Then answer the question.

The Venn diagram which represents the distribution of the participant in the drug trial is attached below. The Number of participants in the drug trial that has anxiety is 370

We can find the number of participants who has dizziness(D). Fatigue(F) and anxiety(A) can be calculated thus :

n(D) = n(D only) + (DnF only) + (DnA only) + (DnAnF)

271 = 36 + 86 + 23 + x

271 = 145 + x

x = 271 - 145

x = 126

n(DnAnF) = 126

Number who has atleast one of the three side effects can be expressed thus :

n(A only) + n(F only) + n(D only) + (DnF only) + (DnA only) + (DnAnF) + n(FnA only) = 585

36 + 23 + 62 + 86 + 126 + 93 + n(FnA) only = 585

n(FnA only) = 585 - 426 = 159

Number of participants who has anxiety can be calculated thus :

n(DnAnF) + (DnA only) + n(FnA only) + n(A only)

126 + 23 + 159 + 62 = 370 participants

Therefore, 370 of the total participants has Anxiety.

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