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Iv) Here, we have a hemophiliac father with a carrier mother. Half the sons are X Yand so are hemophiliacs. The other half of the sons are XY and so are free of the disease. Half the daughters are X X and so will have the disease while the other half are X X and so are carriers. The incidence of hemophilia does not seem to have any strong correlation with ethnicity and about 1 in 5,000 males are born with March 24, 2008 17:9 B-595 ch02 Combining Probabilities 21 the disease. The most famous case of a family history of hemophilia is concerned with Queen Victoria who is believed to have been a carrier.
It will be found that the sum of the probabilities in the second column add to 1 as indeed they must since the mutually exclusive outcomes listed are the totality of possible outcomes. When the ﬁrst game, in which the thrower is not rewarded for multiple 6s, is played 216 times with a unit stake then on 125 occasions the banker wins and on the remaining 91 occasions the thrower wins giving a net loss of 34 stake units. This is shown in the third column of the table. 2. The probabilities for various outcomes of throwing three dice and the expected proﬁts and losses for the thrower for each outcome playing the ﬁrst game 216 times and then playing Crown and Anchor 216 times.
If the arrangement is the top one in Fig. 3, then he will win the money. However, if the arrangement is one of the other two he will ﬁnd a sausage in his box. , 1/3. Next, we assume that he always decides to switch boxes. If the arrangement is the top one then, whichever sausage the host decides to display, our contestant will have picked the other sausage and so by switching he has lost out. But for the Box Probability A B C 1/3 1/3 1/3 Fig. 3. The three possible arrangements of money and sausages, each with probability 1/3.