A company has 1825 employees - Edexcel - A-Level Maths Statistics - Question 5 - 2022 - Paper 1

First, find the total number of non-professional employees. This can be calculated by subtracting the number of professional employees from the total:

$1825 - (740 + 380) = 1825 - 1120 = 705$

Next, to find the number of non-professionals in area B, sum the employees classified as skilled and elementary in area B:

$Skilled_B = 90\quad \text{(from table)}$ $Elementary_B = 80\quad \text{(from table)}$ $Total_{B, not Professional} = 90 + 80 = 170$

The probability is thus:

$P(B | Not Professional) = \frac{170}{705} = 0.241$

1. For Professional (F): In area A, 65% of 740 is 481, and in area B, 65% of 380 is 247. Total in F=481+247=728.

2. For Skilled (R): In area A, 40% of 275 = 110 and in area B, 40% of 90 = 36. Total in H = 110 + 36 = 146.

3. For Elementary (E): In area A, 5% of 260 = 13 and in area B, 5% of 80 = 4. Total in G = 13 + 4 = 17.

4. Venn diagram values can be calculated by considering overlaps based on percentages and direct totals. Please ensure appropriate marking of each region.

To find the intersection of events R and F (those from area A who are professionals), we can use the values derived from the previous calculations. We know that:

Total number of professionals in area A = 740. Thus,

$P(R \cap F) = \frac{380}{1825} \approx 0.208$

To find this probability, apply the formula for the union of two events:

$P(H \cup R') = P(H) + P(R') - P(H \cap R')$

This is calculated based on previous data derived from the Venn diagram.

Using conditional probability: