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A positive integer that reads the same backwards and forwards is called a palindrome. A number greater than 10 and less than $10^{6}$ is choosen at random. If it is known that it is a five digit number and the probability that it is a palindrome is P, then the value of 300 P is equal to.

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answer is 3.

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Detailed Solution

Let A be the even of choosing 5-digit no. and B be the event the number is palindrome (abcba)

$∴ n (A) = 9 (10^{4}) = 90000 A n d n (A \cap B) = 9 \times 10^{2} = 900 P (\frac{E}{A}) = \frac{n (E \cap A)}{n (A)} = \frac{1}{100} = P$

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