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A school employs 75 teachers. The following table summarises their length of service at the school,
classified by gender.


Less than 3 years 3 years to 8 years More than 8 years
Female 12 20 13
Male 8 15 7

(i) Find the probability that a randomly selected teacher:

(I) is female;
(II) is female, given that the teacher has more than 8 years service.

Respuesta :

There are

[tex]12+20+13=45[/tex]

female teachers, and

[tex]8+15+7=30[/tex]

male teachers.

This means that, out of a total of 75 teachers, 45 are female, leading to a probability of

[tex]\dfrac{45}{75}=\dfrac{3}{5}[/tex]

of selecting a female teacher.

If we restrict to those with more than 8 years service, there are 13 female teachers and 7 male teachers.

So, out of a total of 21 teachers, there are 13 female teachers, leading to a probability of

[tex]\dfrac{13}{21}[/tex]

of selecting a female teacher.

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