ch30miscellaneousexamples

ch30miscellaneousexamples - Chapter 30: Miscellaneous...

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Chapter 30: Miscellaneous Examples Example 1(a) : From an ordinary deck of 52 cards, one card is drawn. Find P (Face or Heart). Solution : 26 11 52 3 52 13 52 12 ) ( ) ( ) ( ) ( = - + = - + = H F P H P F P H F P
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Example 1(b) : From an ordinary deck of 52 cards, two cards are drawn. Find P (Both are Kings). Solution : P (Both are K)=P(1 st K and 2 nd K) =P(1 st K) x (2 nd K | 1 st K) 221 1 51 3 52 4 = × =
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Example 2 :Not on final exam A and B take turns to flip a coin, with A first. Who ever gets “heads” first, wins. Find the P(A wins). Solution : Let p=P(A wins). Then p=P(A gets heads at 1 st trial) + P( A gets tails at 1 st trial) x P(B gets tails at 2 nd trial ) x p 3 2 2 3 2 1 4 3 4 1 2 1 2 1 2 1 2 1 = = = + = × × + = p p p p p p p
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B A B H H H’ H H’ H H’ H’ This a limiting sum. Geometric distribution A and B take turns to flip a coin, starting with A. Whoever gets a head first wins. Find the probability that A wins.
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ch30miscellaneousexamples - Chapter 30: Miscellaneous...

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