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# 2005_quiz1 - The University of New South Wales 25 august...

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The University of New South Wales 25 august 2005 ACTl 1001 actuarial studies and commerce quiz one ALL ANSWERS MUST BE WRITTEN IN INK. EXCEPT WHERE THEY ARE EXPRESSLY REQUIRED, PENCILS MAY BE USED ONLY FOR DRAWING, SKETCHING OR GRAPHICAL WORK. &7.& CANDIDATES MAY BRING THEIR OWN CALCULATORS OR HAND HELD COMPUTERS &

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Question 1 [20 marks] Aboxcon ta in s m red and n white balls. Balls are drawn out at random, without replacement. The random variable T ˜ ( r ) is the number of drawings required until r ,1 r m , red balls have been drawn. Show that the probability Pr( k )=Pr { T ˜ ( r )= k } is given by Pr( k )= k 1 r 1 ! m + n k m r ! m + n n ! , for r k n + r. Question 2 [20 marks] A bank sells twenty thousand \$5 notes and subsequently discovers that 150
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2005_quiz1 - The University of New South Wales 25 august...

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