(a) There is a probability of 0.2 that a toy punched by a trainee operator will...

 

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(a) There is a probability of 0.2 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. [5 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. [5 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] (a) There is a probability of 0.2 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. [5 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. [5 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]

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