2. (a) There is a probability of 0.25 that a toy punched by a trainee operator will contain

an error. Find the probability that a random sample of 4 toys punched by a trainee

operator will contain just 1 error-free toy.

[5 marks]

(b) There is a probability of 0.05 that a toy punched by an experienced operator will

contain an error. Find the probability that in a random sample of 20 toys punched by

an experienced operator there will be no more than 3 toys containing errors. [8 marks]

(c) Of the total number of toy punched in a day by a pool of operators, 4% are punched by

trainee operators and 96% by experienced operators. Show that the probability that

a toy chosen at random from a daily output in this pool contains an error is equal to

0.056.

[7 marks]

(d) Given that 2 toys chosen at random from daily output contain error, calculate the

probability that one toy was punched by a trainee operator and the other was punched

by an experienced operator.

[5 marks]

[Q2 Total: 25 marks]