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Nov 2004 p6 q6
2573
A box contains five balls numbered 1, 2, 3, 4, 5. Three balls are drawn randomly at the same time from the box.
(i) By listing all possible outcomes (123, 124, etc.), find the probability that the sum of the three numbers drawn is an odd number.
The random variable \(L\) denotes the largest of the three numbers drawn.
(ii) Find the probability that \(L\) is 4.
Solution
(i) List all possible outcomes of drawing three balls: 123, 124, 125, 134, 135, 145, 234, 235, 245, 345. There are 10 possible outcomes.
To find the probability that the sum is odd, count the outcomes where the sum is odd: 124, 134, 145, 234. There are 4 such outcomes.
The probability is given by \(\frac{4}{10} = 0.4\).
(ii) To find the probability that the largest number \(L\) is 4, consider the outcomes where 4 is the largest: 134, 145, 234, 245. There are 3 such outcomes.
The probability is given by \(\frac{3}{10} = 0.3\).