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New Zealand
Level 8 - NCEA Level 3

Venn Diagrams and Two-Way Tables - Word Problems

Interactive practice questions

At a university there are $816$816 students studying first year engineering, $497$497 of whom are female (set $F$F). $237$237 of these women are studying Civil Engineering, and there are $348$348 students studying Civil Engineering altogether (set $C$C).


State the value of $w$w in the diagram.


State the value of $x$x in the diagram.


State the value of $y$y in the diagram.


State the value of $z$z in the diagram.


What is the probability that a randomly selected male student does not study Civil Engineering?

Approx 9 minutes
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In a group of $69$69 people, $45$45 said they had been to Europe ($E$E) and $26$26 said they had been to Asia ($A$A).

$8$8 people said they had been to neither Europe nor Asia.

$87$87 people are questioned about whether they own a tablet ($T$T) or a smartphone ($S$S). The probabilities shown in the list below were determined from the results.

$100$100 office workers are surveyed about whether they buy a coffee (set $C$C) or lunch (set $L$L) during the work day. Some of the results are shown in the Venn diagram below.



Investigate situations that involve elements of chance: A calculating probabilities of independent, combined, and conditional events B calculating and interpreting expected values and standard deviations of discrete random variables C applying distributions such as the Poisson, binomial, and normal


Apply probability concepts in solving problems

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