Lottery tickets are issued from numbers 1000 to 9999. A person wins the first prize if the number completely matches with number decided by computer. A person wins the second prize if last 3 digits of his ticket number matches. He wins the third prize if last two digits of his ticket number matches with number decided by computer. He wins 4th prize if last digit of his ticket number matches with number decided by computer. If computer decides the winning number is 5678 then the probability of the person winning the lottery is λ Then 100 λ is (Assuming that the person buys only one ticket).

Question

Lottery tickets are issued from numbers 1000 to 9999. A person wins the first prize if the number completely matches with number decided by computer. A person wins the second prize if last 3 digits of his ticket number matches. He wins the third prize if last two digits of his ticket number matches with number decided by computer. He wins 4th prize if last digit of his ticket number matches with number decided by computer. If computer decides the winning number is 5678 then the probability of the person winning the lottery is  λ Then 100 λ  is (Assuming that the person buys only one ticket).

Accepted Answer

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If last digit is 8 (last digit matches only)………..8First place can be filled by 9 waysSecond………………………………10 waysThird……………………………………9 ways∵ 7 (cannot come at tens place)No. of ways  =9×10×9=810Similarly, if last two digits are 78 onlyThen nos.  =9×9=81If last 3 digits matches thenFavorable no’s = 8So favorable cases  =810+81+8+1=900Total cases = 9000Probability =9009000=110

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