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Chapter 3: Q. 3.25 (page 109)
Prove directly that,
By applying the definition of conditional probability,the direction starting from the right side.
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Six balls are to be randomly chosen from an urn containing red, green, and blue balls.
(a) What is the probability at least one red ball is chosen?
(b) Given that no red balls are chosen, what is the conditional probability that there are exactly green balls among the chosen?
Three cards are randomly selected, without replacement, from an ordinary deck of playing cards. Compute the conditional probability that the first card selected is a spade given that the second and third cards are spades.
A and B play a series of games. Each game is independently won by A with probability p and by B with probability 鈭� p. They stop when the total number of wins of one of the players is two greater than that of the other player. The player with the greater number of total wins is declared the winner of the series.
(a) Find the probability that a total of games are played.
(b) Find the probability that A is the winner of the series
A total of percent of the voters in a certain city classify themselves as Independents, whereas percent classify themselves as Liberals and percent say that they are Conservatives. In a recent local election, percent of the Independents, percent of the Liberals, and percent of the Conservatives voted. A voter is chosen at random. Given that this person voted in the local election, what is the probability that he or she is
(a) an Independent?
(b) a Liberal?
(c) a Conservative?
(d) What percent of voters participated in the local election?
You ask your neighbor to water a sickly plant while you are on vacation. Without water, it will die with probability .; with water, it will die with probability .. You are percent certain that your neighbor will remember to water the plant.
(a) What is the probability that the plant will be alive when you return?
(b) If the plant is dead upon your return, what is the probability that your neighbor forgot to water it?
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