Diedre is a head teacher in a school which provides primary, secondary and sixth-form education - AQA - A-Level Maths Pure - Question 13 - 2020 - Paper 3

To find the probability that the teacher is not a sixth-form teacher, we first need to determine the total number of teachers who are in primary and secondary education.

The number of teachers in sixth-form is:

$\text{Sixth-form} = 23 + 24 = 47$

Thus, the total number of teachers who are not in sixth-form is:

$\text{Total Not Sixth-form} = 200 - 47 = 153$

Now, the probability that the teacher selected is not a sixth-form teacher is:

$P( ext{Not Sixth-form}) = \frac{153}{200}$

So, the probability that the teacher selected is not a sixth-form teacher is rac{153}{200}.

To solve this, we first calculate the total number of male teachers:

$\text{Total Male} = 9 + 24 + 23 = 56$

Next, we determine the number of male teachers who are not primary teachers:

$\text{Male Not Primary} = 24 + 23 = 47$

Now we can find the conditional probability:

$P(\text{Not Primary} | \text{Male}) = \frac{\text{Male Not Primary}}{\text{Total Male}} = \frac{47}{56}$

Thus, the probability that a randomly chosen male teacher is not a primary teacher is rac{47}{56}.

To find the probability that all three chosen teachers are secondary teachers, we first determine the total number of secondary teachers:

$\text{Total Secondary} = 24 + 85 = 109$

Next, we calculate the probability for selecting three secondary teachers:

$P(\text{All Secondary}) = \frac{109}{200} \times \frac{108}{199} \times \frac{107}{198}$

Calculating this product gives:

$P(\text{All Secondary}) \approx 0.16$

Therefore, the probability that all three chosen teachers are secondary teachers is approximately $0.16$.