The sample proportion p is an unbiased estimator of the population proportion p no matter what size random sample the polling organization chooses. Explain to someone who knows nothing about statistics why a large random sample will give more trustworthy results than a small random sample.

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

Evaluate 8j -k+148j−k+14 when j=0.25j=0.25 and k=1k=1.

An oil exploration company currently has two active projects, one in asia and the other in europe. let a be the event that the asian project is successful and b be the event that the european project is successful. suppose that a and b are independent events with p(a) = 0.2 and p(b) = 0.8. (a) if the asian project is not successful, what is the probability that the european project is also not successful? (b) what is the probability that at least one of the two projects will be successful? (c) given that at least one of the two projects is successful, what is the probability that only the asian project is successful? (round your answer to three decimal places.)