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Example text

Such a calculation, though, depends upon our assumption of a prior distribution for the composition of the urn (in the preceding section we assumed each ball could be black or white with equal probability). Since we are ignorant about such a distribution, Laplace assumes that all possible compositions of the urn are roughly equally likely. He does this by supposing a large number N + 1 of urns with urn i containing i white and N - i black balls. Select an urn at random, and select n balls within this urn using the procedure of the previous section (selection with replacement).

Conditional Probability: From Kings to Prisoners The sample space for this problem can be considered to be the set S of four pairs (B, B), (B, G), (G, B), (G, G), where B stands for "boy" and G stands for "girl" and the first and second positions in the pair denote first and second born children, respectively. To be able to do the problem some assumptions must be made. Once again, we shall assume each of the four outcomes is equally likely. " What we want to calculate here is P(U/V). Using the formula, we have P(U/V) = P(U n V) = P(one child is B and one is G) = 2/4 = 2/3.

2 Following your dreams in Lottoland I have before me a New York State Lotto ticket for the Pick 6 game. The game is played this way: there is a panel of numbers from 1 to 54. The player marks 6 of these numbers. When the lottery drawing occurs, the player wins (at the first prize level) if all six numbers he chose match the drawn numbers. All the winners split the purse. The minimum play is two game panels for \$1. At the bottom ofthe ticket it says "Follow your dreams ... " What we'd like to do now is investigate if, after following your dreams in Lottoland, you are likely to attain them, or will your dreams be more likely to be so far ahead of you that you will lose them (as well as all the money you gambled away).