Question

If o is the centre of larger circle what is the probability that a point chosen at random within the circumference of the larger circle,lies outside the smaller circle ?
a. 0.33
b. 0.5
c. 0.67
d.0.75​

Answer 1

$\textbf{Given:}$

$\textsf{Radius of the smaller circle is 2 cm}$

$\textbf{To find:}$

$\textsf{Probability of choosing a point lies outside the smaller circle}$

$\textbf{Solution:}$

$\textsf{From the given figure,}$

$\textsf{Radius of the larger circle is, R = 4 cm}$

$\textsf{Radius of the smallerr circle is, r = 2 cm}$

$\textsf{Let E event of choosing a point out of the smaller circle}$

$\textsf{within the circumference of the larger circle}$

$\mathsf{Then,}$

$\mathsf{P(E)=\dfrac{n(E)}{n(S)}}$

$\mathsf{P(E)=\dfrac{\textsf{Area outside the smaller circle}}{\textsf{Area of the larger circle}}}$

$\mathsf{P(E)=\dfrac{\textsf{Area of larger circle-Area of smaller circle}}{\textsf{Area of the larger circle}}}$

$\mathsf{P(E)=\dfrac{\pi\,R^2-\pi\,r^2}{\pi\,R^2}}$

$\mathsf{P(E)=\dfrac{\pi\,(4)^2-\pi\,(2)^2}{\pi\,(4)^2}}$

$\mathsf{P(E)=\dfrac{16\pi-4\pi}{16\pi}}$

$\mathsf{P(E)=\dfrac{12\pi}{16\pi}}$

$\mathsf{P(E)=\dfrac{12}{16}}$

$\mathsf{P(E)=\dfrac{3}{4}}$

$\implies\boxed{\mathsf{P(E)=0.75}}$

$\textbf{Answer:}$

$\textsf{option (d) is correct}$

$\textbf{Find more:}}$

In a class of 78 students 41 are offering French, 22 are offering German. Of the students offering French or German, 9 are offering both courses. What is the probability that none of the students are enrolled in either course?

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In a single throw of two dice,the probability of getting doublet i.e. getting the same number on both dice is(a) 1/2

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Answer 2

Answer:

option d is correct option.

this is your answer buddy.