To get to work, a commuter must cross train tracks. The time the train arrives v

Question

To get to work, a commuter must cross train tracks. The time the train arrives varies slightly from day to day, but the commuter estimates the probability of getting stopped on any working week day is 15%. The commuter goes to work every day during a certain 5-day working week. What is the probability that:

a) The commuter gets stopped on Monday and again on Tuesday?

b) The commuter gets stopped on Monday and does not get stopped on Tuesday and gets stopped on Wednesday?

c) The commuter gets stopped for the first time on Thursday?

d) The commuter gets stopped every day of the 5-day week?

e) The commuter gets stopped at least once during the 5-day week?

Explanation / Answer

as   probability of getting stopped on any working week day is independent on any other work day. Hence

probability that

a) commuter gets stopped on Monday and again on Tuesday =0.15*0.15=0.0225

b) commuter gets stopped on Monday and does not get stopped on Tuesday and gets stopped on Wednesday

=0.15*(1-0.15)*0.15=0.019125

c)commuter gets stopped for the first time on Thursday=P( not getting stopped for first 3 days and gets stopped on thursday) =(1-0.15)3*0.15 =0.0921

d) commuter gets stopped every day of the 5-day week =(0.15)5 =0.0000759

e) commuter gets stopped at least once during the 5-day week =1-P(not getting stopped at allin 5 day)

=1-(1-0.15)5 =0.5563

please revert for any clarification required,

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