144k views
5 votes
The probability that Reece's bus arrives on

time is 3/4

If his bus is on time then the probability he
arrives at work by 9 am is 2/3.

If his bus is late then the probability he arrives
at work by 9 am is 3/10

Work out the probability that Reece does not
arrive at work by 9 am.
Give your answer as a fraction in its simplest
form.

User Resueman
by
8.3k points

1 Answer

3 votes

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.

User Talaya
by
7.9k points