Comparing two bingo cards

Comparing two bingo cards

Secondary 2
5 marks
TGM Original Questions

Core stretch

Balls numbered 1 to 90 are equally likely on the first draw. Two bingo cards contain:

  • Arun: \(4\), \(7\), \(12\), \(18\), \(21\), \(27\), \(33\), \(36\), \(44\), \(52\), \(57\), \(63\), \(68\), \(74\), \(81\), \(88\).
  • Bea: \(2\), \(9\), \(11\), \(16\), \(24\), \(29\), \(35\), \(41\), \(48\), \(54\), \(60\), \(66\), \(72\), \(77\), \(84\), \(90\).
  1. Find the probability that the first number is
    1. on Arun’s card,[1]
    2. a prime on Bea’s card,[1]
    3. greater than 30 on either card,[1]
    4. not on Bea’s card.[1]
  2. Suppose instead that one number is selected at random from the numbers from 1 to 90 that are even or perfect squares. Decide which card it is more likely to appear on.[1]

Solution:

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Answer:(a)(i) \(\frac{8}{45}\) (ii) \(\frac{2}{45}\) (iii) \(\frac{2}{9}\) (iv) \(\frac{37}{45}\) (b) Bea, with \(\frac{11}{50}\) versus \(\frac{10}{50}\).

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