Maths (100 points)

a man finds that he is late for work on 10% of occasions if he was on time the previous day, but late on 20% of occasions if he was late the previous day. given that he was on time on monday and worked on tuesday, what is the probability that he is on time on wednesday? illustrate using a tree diagram

89%

Step-by-step explanation:

If he's on time on the previous day, there's a 10% probability he'll be late, which means there's a 90% probability that he'll be on time.

If he's late on the previous day, there's a 20% probability he'll be late, which means there's a 80% probability that he'll be on time.

He's on time on Monday, so there's a 10% probability he'll be late on Tuesday and a 90% probability he'll be on time.

If he's on time on Tuesday, there's a 10% probability he'll be late on Wednesday and a 90% probability he'll be on time.

If he's late on Tuesday, there's a 20% probability he'll be late on Wednesday and a 80% probability he'll be on time.

So the probability he'll be on time on Wednesday is:

0.10 (0.80) + 0.90 (0.90) = 0.89