The probability that Peter will travel to work by bus on any one day is 0.7

Whenever Peter travels to work by bus, the probability that he will be late is 0.1

Whenever Peter travels to work by bike, the probability that he will be late is 0.05

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 )