1.An audience rating survey of television broadcasting among married couples reveals that the probability of a woman watching a program of fund raising for charity is 0.16,but the probability of a man watching it is 0.23.However,if a woman is watching it,the probability that her husband is also watching is 0.62.If a man is watching the program,what is the probability that his wife is watching together?
2.Bag A contains five similar balls,three of them are red and two yellow;and bag B contains four red and five yellow balls.A ball is drawn at random from A and placed in B;subsequently a ball is drawn at random from B and placed in A.
(a) What is the chance that if a ball is now drawn from A it will be red?
(b) If this ball is in fact red,what is the probability that the first two balls drawn are also red?
3.A plant has spores which is arranged like a linear chain,hence there has three links;the probability of each link breaking is a constant p. If no links break one group is formed,and if one link breaks there are two groups,etc.
Show that the probabilities of one,two,three or four groups being formed are given respectively by (1-p)^3, 3p(1-p)^2, 3p^2(1-p) and p^3.
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更新1:
Answer: 1.0.4313 2.(a)143/250 (b)45/143