A survey of the reading habits of some students revealed that, on a regular basis, 25% read quality newspapers, 45% read tabloid newspapers and 40% do not read newspapers at all - Edexcel - A-Level Maths Statistics - Question 4 - 2007 - Paper 2

To accurately represent the reading habits in a Venn diagram, label the circles as follows:

1. Circle Q for students who read quality newspapers.
2. Circle T for students who read tabloid newspapers.

• The intersection, which represents students who read both types of newspapers, should be labeled with the value 0.10.
• The area exclusive to Circle Q (quality readers) should be labeled with the value $0.25 - 0.10 = 0.15$.
• The area exclusive to Circle T (tabloid readers) should be labeled with the value $0.45 - 0.10 = 0.35$.
• The area outside both circles, which represents students not reading either kind of newspaper, should be labeled as $0.40$.

We are given that this student reads newspapers regularly, which means they are part of the $P(Q \cup T)$ group. We need to find the probability that they only read quality newspapers:

$P(Q \cap T^c | Q \cup T) = \frac{P(Q \cap T^c)}{P(Q \cup T)}.$

Where:

• $P(Q \cap T^c)$ is the probability of reading only quality newspapers, which is $P(Q) - P(Q \cap T) = 0.25 - 0.10 = 0.15.$
• We already established that $P(Q \cup T) = 0.60.$

Now calculating: $P(Q \cap T^c | Q \cup T) = \frac{0.15}{0.60} = 0.25.$

Thus, the probability that this student only reads quality newspapers is 0.25 or 25%.