On any given day, the probability that an employee will drive to work is 0.5, the probabilitythat he/she will cycle to work is 0.3 and the probability that he/she will walk to work is 0.2.If he/she drives, the probability that he/she will arrive on time is 0.6 If he/she cycles, theprobability that he/she will arrive on time is 0.8. If he/she walks, the probability thathe/she will arrive on time is 0.9. An employee is selected at random.a) Calculate the probability that the employee will arrive on time for work.b) If the employee has arrived on time for work yesterday. Calculate the probabilitythat he/she walked to work yesterday.c) The employee has not arrived on time for work yesterday. Calculate the probabilitythat he/she walked to work yesterday.

Jason goes to school either by bus or on foot. If he gets up late in the morning, the probability that he goes by bus is 4/5. If he does not get up late in the morning, the probability that he goes by bus is 1/10. If the probability that he gets up late in morning is 1/20, find the probability that Jason goes to school on foot in a school day.

What is the probability that an employee’s commute time to work is 35 minutes?Note: You’re not expected to know the right answer at this point. This question is given just to get you thinking in the right direction.Approximately 0%Approximately 30%–35%Insufficient information – The probability distribution is required

There are two traffic lights on Fred’s route from home to work. Over the years Fred has tracked when he has to stop at these lights. He determined that 45% of the time he has to stop at the first light; 30% of the time he has to stop at the second light, and 20% of the time he has to stop at both lights.Let A be the event that Fred has to stop at the first light. Let B be the event that Fred has to stop at the second light. What is the probability that Fred has to stop at one or more lights on his way to work?0.6150.550.650.95

A police officer is using a radar device to check motorists’ speeds. Prior to beginning the speed check, theofficer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit.Assuming that the police officer’s estimate is correct, what is the probability that among 4 randomly selectedmotorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit?(A) 0.0256(B) 0.1296(C) 0.3456(D) 0.8704(E) 0.9744

Q5.The probability that it will rain today is 0.5, the probability that it will rain tomorrow is 0.6.The probability that it will rain either today or tomorrow is 0.7.What is the probability that it willrain today and tomorrow?