Final answer:
The probability that Reece does not arrive at work by 9 am is 17/40.
Step-by-step explanation:
To find the probability that Reece does not arrive at work by 9 am, we need to consider two scenarios: when his bus is on time and when his bus is late.
When his bus is on time (with a probability of 3/4), the probability he arrives at work by 9 am is 2/3. Therefore, the probability he does not arrive at work by 9 am when his bus is on time is 1 - 2/3 = 1/3.
When his bus is late (with a probability of 1/4), the probability he arrives at work by 9 am is 3/10. Therefore, the probability he does not arrive at work by 9 am when his bus is late is 1 - 3/10 = 7/10.
Finally, we can calculate the overall probability that Reece does not arrive at work by 9 am by considering the probabilities of these two scenarios:
Probability of Reece's bus being on time * Probability Reece does not arrive at work by 9 am when his bus is on time + Probability of Reece's bus being late * Probability Reece does not arrive at work by 9 am when his bus is late
=(3/4)*(1/3) + (1/4)*(7/10)
= 3/12 + 7/40 = 10/40 + 7/40 = 17/40.