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Probability (p-2) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Probability (p-2)2 Marks
Question
A number of two digits is formed using the digits $1,2,3, \ldots . . ., 9$. What is the probability that the number so chosen is even and less than 60 ?
✓

Answer

The number of two digits can be formed from the given 9 digits in $9 \times 9=81$ different ways.
$
\therefore \mathrm{n}(\mathrm{S})=81
$
Let $\mathrm{A}$ be the event that the number is even and less than 60 .
Since the number is even, the unit place of two digits can be filled in ${ }^4 \mathrm{P}_1=4$ different ways by any one of digits $2,4,6,8$.
Also the number is less than 60 , so tenth place can be filled in ${ }^5 P_1=5$ different ways by any one of the digits $1,2,3,4,5$.
$
\therefore \mathrm{n}(\mathrm{A})=4 \times 5=20
$
$\therefore$ Required probability $=P(A)=\frac{n(A)}{n(S)}=\frac{20}{81}$

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