Download App

PROBABILITY — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPROBABILITY1 Mark
MCQ
Three digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits?
  • A
    $\frac{1}{16}$
  • B
    $\frac{16}{25}$
  • C
    $\frac{1}{645}$
  • ✓
    $\frac{1}{25}$
✓

Answer

Correct option: D.
$\frac{1}{25}$
The given digits are 0, 2, 4, 6, 8.
____ ____ ____
Hundreds Tens Ones
Now, there are 4 ways to fill the hundreds place (0 cannot occupy the hundreds place), 5 ways to fill the tens place and 5 ways to fill the ones place. Total number of 3 digit numbers formed using the given digits = 4 × 5 × 5 = 100 The three digit numbers formed using given digits that have the same digits are 222, 444, 666 and 888 Number of 3 digit numbers that have the same digits = 4 $\therefore$ P(three digit number formed has the same digits) $\frac{\text{Number of 3 digits numbers that have the same digits}}{\text{Total number of 3 digit numbers formed using the given digits}}$ $=\frac{4}{100}=\frac{1}{25}$ Hence, the correct answer is option (d).

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from PROBABILITY→PROBABILITY — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The ratio of the coefficient of terms ${x^{n - r}}{a^r}$and ${x^r}{a^{n - r}}$ in the binomial expansion of ${(x + a)^n}$ will be
→
If the coefficients of the three consecutive terms in the expansion of $(1+ x )^{ n }$ are in the ratio $1: 5: 20$, then the coefficient of the fourth term is $............$.
→
If $a,\;b,\;c,\;d,\;e,\;f$ are in $A.P.$, then the value of $e - c$ will be
→
A and B are two events such that P (A) = 0.25 and P (B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is
→
Two unbiased coins are tossed simultaneously. The probability of getting at least one head is:
→
If $\alpha$ and $\beta$ are the roots of $4x^2+ 3x + 7 = 0$, then the value of $\frac{1}{\alpha}+\frac{1}{\beta}$ is:
→
The sum of the first $20$  terms of the series  $1 + \frac{3}{2} + \frac{7}{4} + \frac{{15}}{8} + \frac{{31}}{{16}} + ...$ is?
→
In a triangle $\tan A + \tan B + \tan C = 6$ and $\tan A\tan B = 2,$ then the values of $\tan A,\,\,\tan B$ and $\tan C$ are
→
The angle between the lines joining the origin to the points of intersection of the straight line $y = 3x + 2$ with the curve $x^2 + 2xy + 3y^2 + 4x + 8y - 11 = 0$ is
→
Let the curve $C$ be the mirror image of the parabola $y^2=4 x$ with respect to the line $x+y+4=0$. If $A$ and $B$ are the points of intersection of $C$ with the line $y=-5$, then the distance between $A$ and $B$ is
→