Download 50 Jahre Deutsche Statistische Gesellschaft Tagungen 1961 PDF

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Hence the same applies to any event with probability unity. Consider the experiment of dealing two cards, at random, from a full deck. Write A = First card is an Ace, B = First card is a Spade, C = Second card is an Ace, D = Second card is a Spade. We can check the working of the definition by verifying that {A, B} are independent, as are {C, D}, {A, D} and {B, C}, but neither {A, C} nor {B, D} are independent. 37 2. Conditional Probability and Independence Suppose we have more than two events.

By the above work, 1. if i > no, then Alex will stick and P(AICi ) = i 2 I K2; 2. if i ::; no, Alex will spin and P(AICi ) = K -0 I: r2. 5 shows that the chance Alex wins is 1 KIno P(A) = K3 L i2 + K4 i=no+l K L L r2. 1 gives some illustrative values. Recall that Alex wins if the scores are tied, but that Bella has the advantage of going second. The table makes sense - Alex's advantage counts for less as K, the number of different scores, increases, and Bella is soon favourite. 1 For various values of K, the optimum tactics for Alex and his winning chances.

What is the chance she selected the double-headed coin? 11. Assume that if a woman carries the gene for haemophilia, any child has a 50% chance of inheriting that gene, and that it is always clear whether or not a son has inherited the gene, but the status of a daughter is initially uncertain. Karen's maternal grandmother was a carrier, the status of her mother in unknown; but Karen's sister Penny has one son, who is healthy. (a) Find the chance that Karen's first child inherits the haemophilia gene.

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