Statistics and Probability Answers

Two events A and B are such that, they are independent and P(A)=x and P(B)=x+0.2 and P(A n B )=0.15. Find;

i) the value of x.

ii) P(A U B) and P( A^c / B^c ), where A^c, B^c are the complements of events A and B respectively.

Supposed that 8P( A U B )=5 and 2x/[P(A)]=1 where P(B) =x.

i) For what values of x are A and B mutually exclusive? For this value of x, are A and B independent?

ii) For what values of x, are A and B independent?

Determine whether for this value of x, A and B are mutually exclusive.

In a bolt manufacturing factory, machines A, B, and C produce 25%, 30% and 45% of the total outputs, respectively. Of their outputs, 7%, 6% and 4% are defective bolt, respectively.

(i) What is the probability that a bolt drawn at random from production will be defective?

(ii) If a bolt drawn at random from production is found to be defective, what is the probability that it was manufactured by machine C?

A blood test indicates the presence of a particular disease 95% of the time when the disease is actually present. The same test indicates the presence of the disease 0.5% of the time when the disease is not present. One percent of the population actually has the disease. Calculate the probability that a person has the disease given that the test indicates the presence of the disease.

Two events E1 and E2 associated with a sample space of an experiment are such that P(E1)=0.27, P(E2)=0.40 and P(E1 U E2)=0.58. Determine whether E1 and E2 are independent.

75% of passengers travelling by metro train wear mask regularly when they travel . A random sample of 500 passengers are selected then find the probability that solution?

A manufacturer of fluorescent bulbs claims that mean life of fluorescent bulb is 400 hours. A sample of 35 fluorescent bulbs was taken and it showed a mean of 399 hours with a standard deviation of 1.1 hours, is the mean life different from 400 hours? Use the 0.05 significance level.