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3 marksDiscrete Random Variables

CAPE Applied Mathematics Unit 2 · 2011 · Paper 2 · Question 3(c)(ii)a)

An experiment consists of drawing, at random, a ball from a box containing 6 red and 3 green balls. A ball is returned to the box if it is red. This process is repeated until a green ball is obtained. Let X represent the number of attempts needed to obtain a green ball.

Determine the probability that it takes EXACTLY 2 attempts to obtain a green ball.

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Other parts of this question

  1. 3(a)(i)Determine the number of different arrangements of the letters of the word MAXIMUM if there are no restrictions.[2 marks]
  2. 3(a)(ii)Determine the number of different arrangements of the letters of the word MAXIMUM if the last letter is a vowel.[3 marks]
  3. 3(a)(iii)Determine the number of different arrangements of the letters of the word MAXIMUM if the 3 M's must be together.[3 marks]
  4. 3(b)A committee of four is to be chosen from 6 men and 4 women. Determine the number of ways that the committee can be chosen so as to contain AT MOST 3 women.[4 marks]
  5. 3(c)(i)Identify the distribution of X and state its parameter(s).[2 marks]
  6. 3(c)(ii)b)Determine the probability that it takes at LEAST 3 attempts to obtain the first green ball.[3 marks]
  7. 3(c)(ii)c)Determine the probability that it takes LESS than 4 attempts to obtain the first green ball.[3 marks]
  8. 3(d)Determine E(X).[2 marks]

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