If O is the centre of the larger circle, what is the probability that point chosen at random within the circumference of the larger circle, lies outside the smaller circle!?
Options: 0.33 , 0.5 , 0.67 and 0.75
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Answers
EXPLANATION.
O is the Centre of a large circle.
Probability that point chosen at random within the circumference of the larger circle lies outside the smaller circle.
As we know that,
Radius of the smaller circle = r = 2 cm.
Radius of the larger circle = R = 4 cm.
Probability = Number of favorable outcomes/Total number of possible outcomes.
⇒ P(E) = n(E)/n(S).
p(E) = Area outside the smaller circle/Area of larger circle.
⇒ p(E) = πR² - πr²/πR².
⇒ p(E) = π(4)² - π(2)²/π(4)².
⇒ p(E) = 16π - 4π/16π.
⇒ p(E) = 12π/16π.
⇒ p(E) = 12/16 = 3/4. = 0.75.
Given :-
If O is the centre of the larger circle,
To Find :-
what is the probability that point chosen at random within the circumference of the larger circle, lies outside the smaller circle!?
Solution :-
Radius of bigger circle = 4
Now,
Area of smaller circle = πr²
Area = π(2)²
Area = π × 4
Area = 4π cm²
Now
Difference of area between larger and smaller circle =
πR² - πr²
π(R² - r²)
π[(4)² - (2)²]
π[16 - 4]
π × 12
12π
PE = F/T
PE = 12π/16π
PE = 12/16
PE = 3/4 or 0.75