Final answer:
The probability that Colin buys a sandwich and gets the bus is found by multiplying the individual probabilities of the two independent events. This gives us a combined probability of 0.21 or 21%.
Step-by-step explanation:
To calculate the probability that Colin buys a sandwich and gets the bus, given that these two events are independent, we use the multiplication rule for independent events. The multiplication rule tells us that if events A and B are independent, then the probability of both A and B occurring (P(A AND B)) is the product of their individual probabilities. Therefore:
- P(Colin buys a sandwich) = 0.3
- P(Colin gets the bus) = 0.7
Since these events are independent, we multiply these probabilities together to find the combined probability:
P(Colin buys a sandwich AND gets the bus) = P(Colin buys a sandwich) × P(Colin gets the bus) = 0.3 × 0.7 = 0.21.
So, the probability that Colin buys a sandwich and gets the bus on the same day is 0.21 or 21%.