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).

Infinity Learn · Accepted Answer

If last digit is 8 (last digit matches only)………..8
First place can be filled by 9 ways
Second………………………………10 ways
Third……………………………………9 ways
$∵$ 7 (cannot come at tens place)
No. of ways $= 9 \times 10 \times 9 = 810$
Similarly, if last two digits are 78 only
Then nos. $= 9 \times 9 = 81$
If last 3 digits matches then
Favorable no’s = 8
So favorable cases $= 810 + 81 + 8 + 1 = 900$
Total cases = 9000
Probability $= \frac{900}{9000} = \frac{1}{10}$

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