Question

1. 4 A box contains 300 discs of different colours. There are 100 pink discs, 100 blue discs and 100 orange discs. The discs of each colour are numbered from 0 to 99. Five discs are selected at random, one at a time, with replacement. Find


(i) the probability that no orange discs are selected. [3]


(ii) the probability that exactly 2 discs with numbers ending in a 6 are selected. [4]


(iii) the probability that exactly 2 orange discs with numbers ending in a 6 are selected. [4]


(iv) the mean and variance of the number of pink discs selected. [8]


1. 5 The mean number of defective batteries in packs of 20 is 1. 6. Use a binomial distribution to calculate the probability that a randomly chosen pack of 20 will have more than 2 defective batteries

Answer 1

The probability that no orange discs are selected is 0.1295 and the probability that exactly 2 discs with numbers ending in a 6 are selected is 0.0721.

How to calculate probability?

The probability that no orange discs are selected will be:

= 200C5 / 300C5

= 0.1295

The probability that exactly 2 discs with numbers ending in a 6 are selected will be:

= (30C2 × 270C3) / (300C5)

= 0.0721

The probability that exactly 2 orange discs with numbers ending in a 6 are selected will be:

= (100C2 × 290C3) / (300C5)

= 0.0092

The mean of the number of pink discs selected will be:

= np

= 5 × 1/3

= 5/3

The variance will be:

= 5 × 1/3 × 2/3

= 10/9 = 1.11

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