Let's solve the given questions step by step.

Given Data:

• $P(\text{car}) = 47\% = 0.47$
• $P(\text{bus}) = 0.13$
• $P(\text{bicycle}) = \frac{3}{10} = 0.30$

a) Calculate $P(\text{car, bus or bicycle})$:

The total probability of choosing one of the three modes of transportation is: $P(\text{car, bus or bicycle}) = P(\text{car}) + P(\text{bus}) + P(\text{bicycle})$

Substitute the values: $P(\text{car, bus or bicycle}) = 0.47 + 0.13 + 0.30 = 0.90$

Answer: $P(\text{car, bus or bicycle}) = 0.90$

b) Did any of the people travel to work in a different way?

The total probability for all possible outcomes should equal 1. Since $P(\text{car, bus or bicycle}) = 0.90$, this leaves a remaining probability of: $1 - 0.90 = 0.10$

This implies that 10% of the people traveled in a different way.

Answer: Yes, 10% of the people traveled in a different way.

Would you like further details or clarification? Here are 5 related questions to expand your understanding:

1. How are probabilities for mutually exclusive events calculated?
2. What would happen if we had overlapping probabilities (e.g., car and bus users)?
3. How would you represent the data in a pie chart to show distribution among these transportation methods?
4. What does the remaining probability (10%) tell us about the possible survey design?
5. How could we model the probability distribution if more transportation methods were included?

Tip: Always ensure the sum of probabilities equals 1 when solving problems involving exhaustive and mutually exclusive events!