A large college produces three magazines - Edexcel - A-Level Maths Statistics - Question 4 - 2021 - Paper 1

From the given probabilities, we know:

$P(G) = 0.25$ $P(G ext{ and } E ext{ and } S) = 0$ This indicates that no students read all three magazines. We also have:

$0.08 + 0.05 + q + p = 0.25$

In this scenario, we can isolate p as:

$p = 0.25 - (0.08 + 0.05 + q)$ $p = 0.12 - q$

To find q, we refer to the Venn diagram, and we find
that:

Thus, the value of p = 0.12.

Returning to the calculation derived from the previously stated equations:

Given: $P(G ext{ and } E) = 0 => q = 0$ Thus, when substituted we get:

$p = 0.12 - 0$
This leads to the final value

Therefore, the value of q = 0.12.

Using the conditional probability formula provided, we know:

$P(S | E) = 5/12$. This can be expressed as:

P(S | E) = rac{P(S ext{ and } E)}{P(E)} This leads us to extract information from the Venn diagram for S and E, and utilizing the provided segment values: From our values, we can infer that:

given P(E) = 0.12

Thus, substituting the values, we isolate r:

$P(S ext{ and } E) = 5/12 * 0.12$ So the final answer for r = 0.10.

From the previous calculations we incorporate:

t = 1 - (0.08 + 0.05 + 0.09 + q + r + p + S)

t = 1 - (0.08 + 0.05 + 0.09 + 0 + 0.10 + 0.12) Calculating this gives:

t = 1 - 0.53 = 0.20

Thus, the value of t = 0.20.

To determine independence: Events A and B are independent if: $P(A ext{ and } B) = P(A) imes P(B)$ Thus we evaluate: P(S ∩ E′) with the respect of G: Using the totals previously established, we compute: P(G) = 0.25; P(S ∩ E′) can be evaluated via Venn proportions available: Given the independent conditions derive: PS(E′)=0.8 Thus, in substitution: P(S ∩ E′) needs comparison to PDestemining the scale of separation. Final determination based on logical derivation shows that events are indeed independent.