(a) 'A' speaks truth in 60 per cent cases and 'B' in 70 per cent cases. In what percent- age of cases are they likely to contradict each other in stating the same fact ? (b) Three groups of workers contain 3 men and 1 woman, 2 men and 2 women, and 1 man and 3 women respectively. One worker is selected at random from each group. What is the probability that the group selected consists of I man and 2 women?

At a class, 80% are female and 40% of the students like to swim. Of the students thatlike to swim, 60% are females. What is the probability that a student chosen at random isa female who likes to swim?

A company did a study of available vacation time for their staff employees over the past years.  They determined the probability a staff employee selected at random has 2 weeks’ vacation was 45%, 1 week vacation 10%, 3 weeks’ vacation 20%, and more than 3 weeks’ vacation was 25%.  The company randomly selects 20 employees.  What is the probability that out of the 20 selected, at least 2 workers have 1 week vacation time?

A bad contains 46 U.S. quarters and 4 Canadian quarters. (The coins are identical in size.) If 4 quarters are randomly picked from the bag, what is the probability of getting at least one Canadian quarter? (Round your answer to kne decimal place.)