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  • Perplex
    IB Math AISL
    /
    Distributions & Random Variables
    /

    Problem Bank

    [Maximum mark: 11]

    At an airport car-rental depot the staff record two events for every car that is returned:

    • C : Car requires exterior cleaning.

    • L : Fuel level is low (below ½ tank).

    From long term data, they estimate that ​P(C)=0.35,P(L)=0.25,​ and ​P(C∩L)=0.12.

    1. Find ​P(C′∩L′)​

      [2]

      To earn a crown, get your answer ready before you reveal the options!

    2. Find the probability that exactly one of the two events occurs.

      [2]
    3. Determine ​P(C∣L).

      [2]
    4. State, and justify, whether events ​C​ and ​L​ appear to be independent.

      [1]

    On a particular day 12 cars are returned.


    Assume that whether any individual car requires exterior cleaning is independent of the others.

    1. State the distribution of the random variable ​X=​ ​number of cars that require cleaning that day.​

      [1]
    2. Find

      1. ​P(X=6).​

        [1]
      2. ​P(X≥4).

        [2]

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