When two people meet, they are sometimes surprised that they have similar beliefs. A survey of 1003 random adults conducted by the Scripps Survey Research Center at Ohio University found that 62 percent of men and 50 percent of women believe in intelligent life on other planets. Well, actually, they said it is either “very likely” or “somewhat likely” that intelligent life exists on other planets (www.reporternews.com).
a. If a man and a woman meet, what is the probability that they both believe in intelligent life on other planets?
b. If a man and a woman meet, what is the probability that neither believes in intelligent life on other planets?
c. What is the probability that the man and woman agree about life on other planets?
d. If a man and a woman meet, what is the probability that they have opposite beliefs on this issue?