Final answer:
The probability that a device using five silicon chips selected randomly from a batch of 100 chips, which includes five defective ones, contains no defective chip is calculated by the ratio of selecting five good chips to selecting any five chips from the batch.
Step-by-step explanation:
The question is asking to find the probability that a device, which uses five silicon chips selected from a batch of a hundred chips with five being defective, will have no defective chip. To solve this, we can calculate the probability step by step using the concept of combinations.
Firstly, we determine the number of ways to select five non-defective chips out of 95 good ones, which is C(95,5). Then, we calculate the total number of ways to select any five chips out of the whole batch, which is C(100,5). The probability that the device contains no defective chip is the ratio of these two numbers:
P(device has no defective chip) = C(95,5) / C(100,5)
Where C(n,k) represents the number of combinations of n items taken k at a time.
To calculate this, use factorials where C(n,k) = n! / [(n-k)!k!].
So, the probability that the device contains no defective chip, is:
P(device has no defective chip) = (95! / (90!*5!)) / (100! / (95!*5!))
Simplifying the factorials, we have:
P(device has no defective chip) = (95*94*93*92*91) / (100*99*98*97*96)
Finally, calculate this to get the decimal value, which would give the probability that the device contains no defective chips when made up from one batch.