Question

An airline claims that 90% of the time, its planes are on schedule. If three flights are selected at random, what is the probability that the first two are on schedule and the third one is not on schedule?

Answer 1

1. Check the tree diagram in the picture attached.

2. The blue segment represents "on time"
    The red segment represents "not on time"


3. blue - blue - red represents the case 1st on time, 2nd on time, 3rd not on time.

the combined probability is 90/100*90/100*10/100=9/10*9/10*1/10=99/1000=0.099

4. Remark with a tree diagram we can tell anything asked about the probability of an experiment.