Multiple choice

A box contains 15 lead balls of which 5 are white lead balls. If 5 lead balls are selected at random from the box, what is the probability that at least one of them is white lead balls ?

  1. 91/143

  2. 101/143

  3. 111/143

  4. 121/143

  5. 131/143
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

P(at least 1 white) = 1 - P(no white) = 1 - P(all 5 are non-white). There are 10 non-white balls. P(all non-white) = C(10,5)/C(15,5) = 252/3003. Therefore P(at least 1 white) = 1 - 252/3003 = 2751/3003 = 131/143. Using the complement is easier than counting directly.

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