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What's the chances of being late for work.

Peter travels to work either by bus or by bike

Given facts

  1. The probability that Peter will travel to work by bus on any one day is 0.7
  2. Whenever Peter travels to work by bus, the probability that he will be late is 0.1
  3. Whenever Peter travels to work by bike, the probability that he will be late is 0.05
  4. Peter is going to go to work on Monday and on Tuesday.
What is the probability that he will be late for work on at least one of these days.

Answer

By Bus On his bike
Probablility
of going by ...
0.7 0.3
Probablility
of being late on one day
(Either Monday OR Tuesday)
AND he went by ..
0.7 x 0.1 = 0.07 0.3 x 0.05 = 0.015
0.7 x 0.1 = 0.07
Probablility
of not being late on a day
(Either Monday OR Tuesday)
AND he went by ..
1 - 0.07 = 0.93 1 - 0.015 = 0.985
Probability
of not being late on a day
( Combined events )
As the days increase, the probability gets less
By bus or on his bike
0.93 x 0.985 = 0.91605
Probability
of not being late
BOTH DAYS
0.91605 x 0.91605 = 0.8391476025
Probability
of being late
ON EITHER DAY
1 - 0.8391476025 = 0.1608523975
( Because he must either be late on one of those days or not late on either of those days, MUST or certainty has a probability = 1
Prob' late on at least one day = 2 x ( 0.085 x 0.915 )




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