Figure 1 shows how 25 people travelled to work - Edexcel - A-Level Maths Statistics - Question 4 - 2012 - Paper 2

To determine if events B and T are independent, we check if the occurrence of one affects the probability of the other. Given the information, we have:

• Total occurrences for B and T are 4 and 3 respectively.
• The joint occurrence of B and T is 0 (as no one rides both). Hence,

Using the formula for independence: $P(B \cap T) = P(B) \cdot P(T)$

Calculate:

• $P(B) = \frac{4}{25}$
• $P(T) = \frac{3}{25}$
• $P(B \cap T) = 0$

So, since the probabilities do not satisfy the independence condition, B and T are not independent.

The total number of people who walk is represented by the event W, which is 7. Therefore, the probability that a randomly chosen person walks to work is $P(W) = \frac{7}{25} = 0.28$.

Since no individual can travel using both B and T at the same time (mutually exclusive), the probability of traveling by both bicycle and train is: $P(B \cap T) = 0$.

Using conditional probability, we need to find: $P(T | B) = \frac{P(T \cap B)}{P(B)}$

• We established that $P(T \cap B) = 0$ and $P(B) = \frac{4}{25}$.

Thus, $P(T | B) = \frac{0}{\left(\frac{4}{25}\right)} = 0.$ Therefore, if a person travels by bicycle, the probability of them also taking the train is 0.