Question

There are two concentric
circles A and B, of radius 5
and 10 cm respectively, on
a board for a contest of
archery. An arrow shot by
Yajuvendra will certainly
hit inside the larger circle.
Find the probability of the following events.
(1) The arrow will hit inside the circle A.
(2) The arrow will hit between the two circles A and B.​

Answer 1

Answer:

Step-by-step explanation:

Answer: 1. 0.25 and 2. 0.75.

Step-by-step explanation: As shown in the attached figure, we are given two concentric circles A and B with centre 'O', radius 5 cm and 10 cm respectively.

So, area of circle A is given by

a_1=\pi\times 5^2=25\pi

and

area of circle B is

a_2=\pi\times 10^2=100\pi.

So, the areq lying between circle A and B is

a_3=a_2-a_1=75\pi.

Therefore, the probability that the arrow will hit inside circle A is

p_1=\dfrac{25\pi}{25\pi+75\pi}=\dfrac{1}{4}=0.25

and the probability that the arrow will hit between the two circles A and B is

p_2=\dfrac{75\pi}{25\pi+75\pi}=\dfrac{3}{4}=0.75.

Thus, the probabilities are 0.25 and 0.75.

hope it was helpful

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