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21 January, 09:56

A total of 4 buses carrying 148 students from the same school arrive at a football stadium. The buses carry, respectively, 40, 33, 25, and 50 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying this randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on her bus. What is E[X+Y]?

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  1. 21 January, 10:26
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    76.2838

    Step-by-step explanation:

    E[X+Y] = E[X] + E[Y]

    E[X] is the average of X or expectancy of X

    E[Y] is the average or expectancy f Y

    E[X] = 40P (student is in bus 1) + 33P (student is in bus 2) + 25P (student is in bus 3) + 50P (student is in bus 4) =

    40 (40/148) + 33 (33/148) + 25 (25/148) + 50 (50/148) = 39.2838

    E[Y] = (number of students) / (number of drivers) = 148/4 = 37

    So E[X+Y] = 39.2838 + 37 = 76.2838
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