NECO 2023 · Paper 2 · Q5

In a certain school, the principal gave the analysis of the qualified subject teachers as follows.

Subject	English	Mathematics	Physics	French	Biology
No. of teachers	10	8	4	6	12

(a)
Draw a pie chart to illustrate this information. (Enter the sector angles for English, Mathematics, Physics, French and Biology.)
Separate values with commas, e.g. 3, −2
(b)
If two teachers are chosen to represent the school at a workshop, what is the probability that both come from Physics or both from Biology?

Worked solution (try it first)

(a)

There are $10 + 8 + 4 + 6 + 12 = 40$ teachers, and the whole circle is $360^\circ$ , so each teacher gets $\frac{360^\circ}{40} = 9^\circ$ .
The sector angles are English $10 \times 9^\circ = 90^\circ$ , Mathematics $72^\circ$ , Physics $36^\circ$ , French $54^\circ$ and Biology $108^\circ$ .
Check: $90 + 72 + 36 + 54 + 108 = 360$ .
Draw the sectors with a protractor and label each with its subject and angle.

(b)

The two teachers are chosen one after the other from 40, so the second is chosen from the 39 left.
Both from Physics: $\frac{4}{40} \times \frac{3}{39} = \frac{12}{1560}$ .
Both from Biology: $\frac{12}{40} \times \frac{11}{39} = \frac{132}{1560}$ .
These can't both happen, so add: $\frac{12 + 132}{1560} = \frac{144}{1560}$
$= \frac{6}{65}$ .

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