MHT CET · Maths · Probability
A box contains 100 tickets numbered 1 to 100 . A ticket is drawn at random from the box. Then the probability, that number on the ticket is a perfect square, is
- A \(\frac{1}{10}\)
- B \(\frac{3}{10}\)
- C \(\frac{7}{100}\)
- D \(\frac{9}{100}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{10}\)
Step-by-step Solution
Detailed explanation
Let \(X\) : Event that number on the ticket is perfect square.
\(\therefore \mathrm{X}=\{1,4,9,16,25,36,49,64,81,100\}\)
\(\therefore \mathrm{n}(\mathrm{X})=10\)
\(\text {Also, } \mathrm{n}(\mathrm{S})=100\)
\(\therefore\) Required probability \(=\frac{\mathrm{n}(\mathrm{x})}{\mathrm{n}(\mathrm{S})}=\frac{10}{100}=\frac{1}{10}\)
\(\therefore \mathrm{X}=\{1,4,9,16,25,36,49,64,81,100\}\)
\(\therefore \mathrm{n}(\mathrm{X})=10\)
\(\text {Also, } \mathrm{n}(\mathrm{S})=100\)
\(\therefore\) Required probability \(=\frac{\mathrm{n}(\mathrm{x})}{\mathrm{n}(\mathrm{S})}=\frac{10}{100}=\frac{1}{10}\)
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