B3. (a) The village of Sunnyridge has installed an array of 6 wind turbines. The probability of any day being insufficiently windy for the turbines to operate is found to be 0.3. The probability on any day that any individual turbine needs to be shut down for maintenance is found to be 0.1. [You may assume that all probabilities are mutually independent] A monitoring device is mounted upon one of the wind turbines. (i) What is the probability that the monitored wind turbine operates on any given day? (ii) The monitored turbine is observed to be not operating. What is the proba- bility that this turbine has been shut down for maintenance? (iii) What is the probability that more than 2 of the 6 turbines are shut down for maintenance on any particular day? (iv) What is the probability that at least 4 turbines are operating on any particular day? (b) Sunnyridge decide to additionally install a solar energy plant. From prior weather records, it is estimated that the number of hours per day of sunshine at Sunnyridge S is a random variable that obeys a probability density function 0≤s<2 ½ fs(s) = 12 s 70 2≤8<12. 0 otherwise (i) What is the probability of less than 4 hours of sunshine on any given day? (ii) Find the mean and variance of the number of hours of daylight. (iii) Find the probability of there being less than 1400 hours of sunshine in a year.

Given the probability that "she's up all night 'til the sun" OR "she's up all night for good fun" is 0.34, the probability that "she's up all night for good fun" is 0.08, and the probability that "she's up all night 'til the sun" AND "she's up all night for good fun" is 0.34, what's the probability that "she's up all night 'til the sun"?

I need help with a, b, c and d.

D An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil) = 0.40 P(medium-quality oil) = 0.25 P(no oil) = 0.35 a. What is the probability of finding oil (to 2 decimals)? b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below. P(soil|high-quality oil) = 0.25 P(soil|medium-quality oil) = 0.90 P(soil|no oil) = 0.25 %3D Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals). P(high-quality oil|soil) P(medium-quality oil soil) P(no oil soil) What is the new probability of finding oil (to 4 decimals)? According to the revised probabilities, what is the quality of oil that is most likely to be found? - Select your answer -