Question

Numbers $1$ to $10$ are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of .

1. getting a number $6$?
2. getting a number less than $6$?
3. getting a number greater than $6$?
4. getting a $1$-digit number?

Answer 1

(i) Outcome of getting a number $6$ from ten separate slips is one.
Therefore, probability of getting a number $6$ = $\frac{1 }{10}$

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(ii) Numbers less than $6$ are $1, 2, 3, 4$ and $5$ which are five.
So there are $5$ outcomes.
Therefore, probability of getting a number less than $6$ = $\frac{5}{10}$ = $\frac{1}{2}$

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(iii) Number greater than $6$ out of ten that are $7, 8, 9, 10$.
So there are $4$ possible outcomes.
Therefore, probability of getting a number greater than $6$ = $\frac{4}{10}$ = $\frac{2}{5}$

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(iv) One digit numbers are $1, 2, 3, 4, 5, 6, 7, 8, 9$ out of ten.
Therefore, probability of getting a $1$-digit number
= $\frac{9 }{10}$