I have this question that's bugging me and will be grateful if someone can show me the caliculations also so that I can do others on my own bat. "David Brain, CEO of ACME STAINELSS STEEL INC, has appointed you as an environmental consultant to assess the possibility of a serious accident. You assess the chance of a serious accident in any particular month is about 2%. Find the probability there will be no spills over a six-month period." Thanks. Daniel
The probability of no "spills" (serious accidents) in one month is 0.98. For six months, it is (0.98)^6 = 88.6%
To calculate the probability of no spills over a six-month period, you can use the concept of independent events and multiply the individual probabilities for each month together.
Given that the chance of a serious accident in any particular month is about 2% or 0.02, the probability of no spills in one month would be the complement of that, which is 1 - 0.02 = 0.98.
To find the probability of no spills over a six-month period, you need to calculate (0.98)^6. Raise the probability of no spills in one month (0.98) to the power of 6 because you are considering six months.
Calculating (0.98)^6 can be done by multiplying 0.98 by itself six times:
(0.98) x (0.98) x (0.98) x (0.98) x (0.98) x (0.98) = 0.941192.
So, the probability of no spills over a six-month period is approximately 0.941192, or 94.1%.
Therefore, there is a 94.1% probability that there will be no spills over a six-month period.