Homework/math

Question

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 he will get stopped on about18% of work days. Which of the following statement (s) is (are) true. Select all that apply. A) During a certain 5-day (Monday – Friday) work week, the probability that he getsTo get to work, a commuter must cross train tracks. The time the train arrives varies slightly from day to day, but the commuter estimates he will get stopped on about18% of work days. Which of the following statement (s) is (are) true. Select all that apply.
A)During a certain 5-day (Monday – Friday) work week, the probability that he gets stopped every day is 0.0001889568.
B)During a certain 5-day (Monday – Friday) work week, the probability that he gets stopped for the first time on Thursday is 0.0992.
C)During a certain 5-day (Monday – Friday) work week, the probability that he gets stopped on Monday and again on Tuesday is 0.0324.
D)During a certain 5-day (Monday – Friday) work week, the probability that he gets stopped at least once during the week is 0.6293

Let X be the random variable denoting a commuter will get stopped on a working day.

P(X) = 0.18

a) Hence the probability that he gets stopped every day starting from Monday to Friday is = P(X)^5 = 0.18^5

Hence option a be the correct answer.

b) Hence the probability that he gets stopped for the first time on Thursday is = (1-P(X))^3*P(X) = (1-0.18)^3*0.18 = 0.0992

Hence b is also correct.

c) The probability that he gets stopped on Monday and again on Tuesday is = P(X)^2 = 0.0324

Hence option c is also correct.

d) The probability that he gets stopped at least one day in 5 working days =

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