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  • Perplex
    IB Math AIHL
    /
    Probability
    /

    Problem Bank

    [Maximum mark: 6]

    In a robotics lab there are nine identical data-sticks, each labelled with a single code letter:


    <p>The diagram shows nine identical circles (nodes), each containing a single letter. They are laid out in two staggered rows:</p>
<p>• Top row (left to right): A, A, A, I   (and, set slightly apart to the right, X)<br>
• Bottom row (left to right): O, R, T, T</p>
<p>Altogether the multiset of labels is {A, A, A, I, O, R, T, T, X}. There are no lines or arrows—just the nine labeled circles.</p>

    A technician randomly selects two sticks, without replacement.

    1. Find the probability that the first stick selected is labelled

      1. ​A,

        [1]

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

      2. ​A​ or ​I.

        [1]
    2. Determine the probability that the second stick selected is labelled ​A, given that the first stick selected was labelled ​I.

      [2]
    3. Find the probability that both sticks selected are labelled ​A.

      [2]

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