Download App

Probability — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsProbability1 Mark
MCQ
Three integers are chosen at random from the first 20 integers. The probability that their product is even is:
  • A
    $\frac{2}{19}$
  • B
    $\frac{3}{29}$
  • ✓
    $\frac{17}{19}$
  • D
    $\frac{4}{19}$
✓

Answer

Correct option: C.
$\frac{17}{19}$
Number of ways in which we can choose three distinct integers from 20 integers $\ ^{20}\text{C}_3=1140$
We know that, if we take three odd numbers, there product will always be an odd number.
Out of 20 consecutive integers, 10 are even and 10 are odd integers.
Number of ways in which we can choose three distinct odd integers from 10 odd integers $=\ ^{10}\text{C} _3=120$
P(product is even) = 1 - P(product is odd),
$=1-\frac{120}{1140}=\frac{1140-120}{1140}=\frac{1020}{1140}=\frac{17}{19}$

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 "M.C.Q (1 Marks)" from Probability→Probability — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The numbers of arrangements of the letters of the word $SALOON$, if the two $O's$ do not come together, is
→
If $\big(4^3\big)\big(4^6\big)\big(4^9\big)\big(4^{12}\big)\ \dots\big(4^{3\text{x}}\big)=(0.0625)^{-54},$ the value of x is:
→
If $\tan\Big(\frac\pi4+\text{x}\Big)+\tan\Big(\frac\pi4-\text{x}\Big)=\text{a},$ then $\tan^2\Big(\frac\pi4+\text{x}\Big)+\tan^2\Big(\frac\pi4-\text{x}\Big)=$
→
From the point $(-1, 2)$ tangents are drawn to parabola $y^2 = 4x$, then the area of the  triangle formed by the chord of contact and the tangent is-
→
Then sum $\sum\limits_{k = 1}^{20} {k\frac{1}{{{2^k}}}} $ is equal to
→
If $2(y - a)$ is the $H.M.$ between $y - x$ and $y - z$, then $x - a,\;y - a,\;z - a$ are in
→
Which of the following functions have the maximum value unity ?
→
The argument of $\frac{1-\text{i}\sqrt{3}}{1+\text{i}\sqrt{3}}$ is:
→
Consider the numbers $1, 2, 3, 4, 5, 6, 7, 8, 9, 10.$ If $1$ is added to each number, the variance of the numbers so obtained is:
→
If the ${5^{th}}$ term of a $G.P.$ is $\frac{1}{3}$ and ${9^{th}}$ term is $\frac{{16}}{{243}}$, then the ${4^{th}}$ term will be
→