The Venn diagram shows information about \(80\) people. \(46\) of them speak French, \(38\) speak Spanish and \(15\) speak both French and Spanish. (a) Writ...
Question 1 Report
The Venn diagram shows information about \(80\) people. \(46\) of them speak French, \(38\) speak Spanish and \(15\) speak both French and Spanish.
(a) Write down the number of people who speak French but not Spanish. [1]
(b) Find the number of people who speak neither French nor Spanish. [2]
(c) One of the \(80\) people is chosen at random. Write down the probability that this person speaks Spanish. [1]
Answer Details
(a) The \(46\) French speakers include the \(15\) who also speak Spanish. Removing them leaves the French-only region.
\[ 46 - 15 = 31 \text{ people} \] [B1]
(b) Adding the two language totals counts the \(15\) bilingual people twice, so subtract the overlap once to get the number who speak at least one language.
\[ 46 + 38 - 15 = 69 \text{ people speak French or Spanish or both} \] [M1]
\[ 80 - 69 = 11 \text{ people speak neither} \] [A1]
(c) All \(38\) Spanish speakers count here, whether or not they also speak French, out of the \(80\) people:
\[ P(\text{Spanish}) = \frac{38}{80} = \frac{19}{40} \] [B1]
Equivalent forms such as \(\frac{38}{80}\) or \(0.475\) are accepted. The completed diagram has \(31\) French only, \(15\) both, \(23\) Spanish only and \(11\) neither, and these four regions add to \(80\), which is the check worth doing before writing any answers.
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