An integer is chosen at random from first 200 positive integers. … - Vidyadip

Question

An integer is chosen at random from first 200 positive integers. Find the probability that the integer is divisible by 6 or 8.

✓

Answer

Let A be the event of choosing a positive integer divisible by 6
$\therefore\text{A}=\{6,\ 12,\ ....,\ 198\}$
$\Rightarrow\text{n}(\text{A})=33$
$\therefore\text{p}(\text{A})=\frac{33}{200}$
Let B be the event of choosing a positive integer divisible by 8
$\therefore\text{B}=\{8,\ 16,\ ....,\ 200\}$
$\Rightarrow\text{n}(\text{B})=25$
$\therefore\text{p}(\text{B})=\frac{25}{200}$
Also, $\text{A}\cap\text{B}=\{24,\ 28,\ ...,\ 192\}$
$\Rightarrow\text{n}(\text{A}\cap\text{B})=8$
$\therefore\text{p}(\text{A}\cap\text{B})=\frac{8}{200}$
$\therefore\text{p}(\text{A}\cup\text{B})=\frac{1}{4}$

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 "5 Marks Questions" from Probability→Probability — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow1}\frac{\sqrt{5\text{x}-4}-\sqrt{\text{x}}}{\text{x}-1}$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{5\text{x}+4\sin3\text{x}}{4\sin2\text{x}+7\text{x}}$

Prove that:
$\frac{\sin5\text{A}-\sin7\text{A}+\sin8\text{A}-\sin4\text{A}}{\cos4\text{A}+\cos7\text{A}-\cos5\text{A}-\cos8\text{A}}=\cot6\text{A}$

Solve the following equations:
$\sin\text{x}\ \tan\text{x}-1\tan\text{x}-\sin\text{x}$

If S₁, S₂, S₃, be respectively the sums of n, 2n, 3n terms of a G.P., then prove that $\text{S}^2_1+\text{S}^2_2=\text{S}_1(\text{S}_2+\text{S}_3).$

If $\theta$ lies in the first quadrant and $\cos\theta=\frac{8}{17},$ then find the value of $\cos(30^\circ+\theta)+\cos(45^\circ-\theta)+\cos(120^\circ-\theta).$

$\sin(\text{B}-\text{C})\cos(\text{A}-\text{D})+\sin(\text{C}-\text{A})\\\cos(\text{B}-\text{D})+\sin(\text{A}-\text{B})\cos(\text{C}-\text{D})=0$

In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows:

French = 17, English = 13, Sanskrit = 15

French and English = 09, English and Sanskrit = 4

French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study.

French only.
English only.
Sanskrit only.
English and Sanskrit.
French and Sanskrit but not English.
French and English but not Sanskrit.
At least one of the three languages but not French.
None of the three languages.

In a $\triangle\text{ABC},$ if $\cos\text{C}=\frac{\sin\text{A}}{2\sin\text{B}},$ prove that the triangle is isosceles.

Let P(n) be the statement: $2^{\text{n}}\geq3\text{n}.$ If p(r) is true, Show that p(r + 1) is true. Do you conclude that p(n) is true for all $\text{n}\in\text{N}$?