1. The Venn diagram shows the probabilities associated with four events, A, B, C and D - Edexcel - A-Level Maths Statistics - Question 1 - 2020 - Paper 1

To find the value of p, we can use the total probability for event B:

$P(B) = 0.4 = 0.07 + p + 0.24 + q$

From the Venn diagram:

$0.4 = 0.07 + p + 0.24 + (0.16 + q)$

We know from logical reasoning that:

$q = 0.20$

Thus,

$p = 0.09$.

Since A and B are independent, we have:

$P(A ext{ and } B) = P(A) imes P(B)$

From the Venn diagram, we know:

$P(A) = 0.24 + 0.20 + 0.07 + 0.16 = 0.67$

Thus,

$P(A) imes P(B) = 0.67 imes 0.4 = 0.268$

The value of q previously is confirmed as 0.20.

(i) To find the value of r, we can use the formula:

$P(B'|C) = \frac{P(B' \cap C)}{P(C)}$

From probability:

$0.64 = \frac{r}{r + 0.25 + s}$ So, we can express it as:

$r = 0.64(r + 0.25 + s)$

(ii) Finding the value of s using:

Using total probabilities yields further equations:

\Rightarrow s = 0.08$$.