Question

The probablity that masons bus arrives on time is 4/5 if his bus is on time then the probablity he arrives at work by 9 am is 3/4 if his bus is late then the porbablity he arrives at work by 9 am is 3/10.

work out the porbability that mason does not arrive at work by 9 am give your answer as a fraction in its simplest form

Answer 1

The probability that Mason does not arrive at work by 9 am is 17/50. This is calculated by considering the scenarios where his bus is on time or late and computing the respective probabilities of not arriving on time.

Step-by-step explanation:

To calculate the probability that Mason does not arrive at work by 9 am, we need to consider two scenarios: when his bus is on time and when it is late.

Scenario 1: The bus is on time (with a probability of 4/5). If the bus is on time, the probability that Mason still does not make it to work by 9 am is the complement of him arriving on time, which is 1 - (3/4) = 1/4.

Scenario 2: The bus is late (with a probability of 1/5, since probabilities sum to 1 and the bus being on time is 4/5). If the bus is late, the probability that Mason does not make it to work by 9 am is 1 - (3/10) = 7/10.

Now, using the Law of Total Probability, we combine these two scenarios:

• Probability (Bus on time) * Probability (Not arrive on time given bus on time)
• + Probability (Bus late) * Probability (Not arrive on time given bus late)

This yields (4/5)*(1/4) + (1/5)*(7/10), which simplifies to (4/20) + (7/50) = (10/50) + (7/50) = 17/50.

Therefore, the probability that Mason does not arrive at work by 9 am is 17/50.