Solution for the Question in the Uploaded Image:

We are tasked to calculate:

(a) The probability that, on a randomly chosen day, Parveen will travel by bus and be late for school.

Step 1: Given probabilities

1. Probability that Parveen travels by bicycle ($P(\text{Bicycle})$):
   $P(\text{Bicycle}) = 0.7$ Thus, the probability that Parveen travels by bus is:
   $P(\text{Bus}) = 1 - P(\text{Bicycle}) = 1 - 0.7 = 0.3$

2. Probability that Parveen is late for school when traveling by bus ($P(\text{Late}|\text{Bus})$):
   $P(\text{Late}|\text{Bus}) = 0.1$

Step 2: Formula for probability of traveling by bus and being late

The probability of two events happening together is given by the multiplication rule: $P(\text{Bus and Late}) = P(\text{Bus}) \times P(\text{Late}|\text{Bus})$

Step 3: Substituting the values

$P(\text{Bus and Late}) = 0.3 \times 0.1 = 0.03$

Final Answer:

The probability that Parveen will travel by bus and be late for school is: $\boxed{0.03 \, \text{(or 3\%)}}.$

Do you want further clarifications or detailed steps? Here are 5 related questions:

1. How do we calculate the probability of not being late for school using similar data?
2. What is the total probability that Parveen will be late (using both bus and bicycle scenarios)?
3. Can we verify the calculation using a tree diagram?
4. How does conditional probability apply in this problem?
5. If the probabilities change, how does it impact the outcomes?

Tip: Always ensure probabilities for all possible outcomes sum to 1 for correctness.