If a part on a production line is present in an inspection area, a sensor detects it with probability 0.99. If a part is not present, the sensor generates a false alarm with probability 0.02. Assume that the probability of a part being present is 0.1.a) What is the probability of seeing a false alarm?b) What is the probability of having a missed detection?

a) P=0.018

b) P=0.001

Step-by-step explanation:

The probability of a false alarm is equal to the probability of not having a part (0.9) multiplied by the probability of generating a alarm if there is no part (0.02).

The probability of having a missed detection is equal to the probability of having a part (0.1) multiplied by the probability of not detecting it if it is there (0.01).

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.