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9 Microchips are mass-produced on a production line.
The probability of a microchip functioning is 0.9, and all microchips are independent.
(i) For any pair of microchips, calculate the probability that at least one of the pair will function. ...................................................[2]
Three different designs of an electronic component are to be made using these microchips.
Design A contains 3 microchips, all of which must function to enable the component to function. Design B contains 6 microchips arranged in two sets of three. Provided at least one set of three all function, the compounent will function.
Design C contains 6 microchips arranged in three pairs. Provided at least one microchip of each pair functions, the component will function.
(ii) Calculate the probability that a component will function if it is of either
1.Design A
2.Design B
3. Design C
(iii) 6000 microchips have been produced.
Find which of the three designs would be expected to produce the highest number of functioning components from these microchips, and state what that number is.
4040/23/O/N/12
The probability of a microchip functioning is 0.9, and all microchips are independent.
(i) For any pair of microchips, calculate the probability that at least one of the pair will function. ...................................................[2]
Three different designs of an electronic component are to be made using these microchips.
Design A contains 3 microchips, all of which must function to enable the component to function. Design B contains 6 microchips arranged in two sets of three. Provided at least one set of three all function, the compounent will function.
Design C contains 6 microchips arranged in three pairs. Provided at least one microchip of each pair functions, the component will function.
(ii) Calculate the probability that a component will function if it is of either
1.Design A
2.Design B
3. Design C
(iii) 6000 microchips have been produced.
Find which of the three designs would be expected to produce the highest number of functioning components from these microchips, and state what that number is.
4040/23/O/N/12