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2026 NYGH P1 Q3

2026 NYGH P1 Q3

IP 4
7 marks

Andy rolls a fair 6-sided die. Depending on the outcome of the roll, he proceeds to select two toy animals from either Box \(X\) or Box \(Y\).

Box \(X\) contains 5 bears and 7 lions.

Box \(Y\) contains 8 bears and 10 lions.

If he rolls an even number, he selects one toy at random from Box \(X\), followed by a toy from Box \(Y\).

If he rolls an odd number, he selects two toys from Box \(X\), at random, without replacement.

  1. Complete the tree diagram to represent the outcomes.[2]
    \(\left(\dfrac{1}{2}\right)\)
    Even
    \(\left(\dfrac{1}{2}\right)\)
    Odd
    \(\left(\dfrac{5}{12}\right)\)
    Bear
    \(\left(\dfrac{7}{12}\right)\)
    Lion
    \(\left(\dfrac{5}{12}\right)\)
    Bear
    \(\left(\dfrac{7}{12}\right)\)
    Lion
    \(\left(\dfrac{4}{9}\right)\)
    Bear
    \(\left(\dfrac{5}{9}\right)\)
    Lion
    \(\left(\dfrac{4}{9}\right)\)
    Bear
    \(\left(\dfrac{5}{9}\right)\)
    Lion
    \(\left(\phantom{\dfrac{0}{00}}\right)\)
    Bear
    \(\left(\phantom{\dfrac{0}{00}}\right)\)
    Lion
    \(\left(\phantom{\dfrac{0}{00}}\right)\)
    Bear
    \(\left(\phantom{\dfrac{0}{00}}\right)\)
    Lion
    Dice Roll
    1st toy
    2nd toy
  2. Find the probability that he selected
    1. two bears,[2]
    2. two different animals.[3]

Solution:

Solution locked

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Answer:(a) Odd-roll second-toy branches: \(\dfrac4{11},\dfrac7{11},\dfrac5{11},\dfrac6{11}\) (b)(i) \(\dfrac{50}{297}\) (ii) \(\dfrac{1213}{2376}\)

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