## Jagat Chaudhary is teaching live on Unacademy Plus

IIT-JEE (main +Advanced) Probability On

Conh nuous Sample Space

Con- nous Sample Shace sf a boint is taken at vandom en area S hich includes an area othe chane-hatbont falls on a

dtCorn nuous Sample space of a point is tiken at vandom em area S which includes an area the chane- hat bont fals ona

Ques: A sphere is circumscribed over a cube. Find the Prob That a point lies inside the sphere, lies outside the cube

Ques: A sphere is circumscribed over a cube. Find the Prob That a point lies inside the sphere, lies outside the cube Solution Required probability favorable volume total volume

Ques: A sphere is circumscribed over a cube. Find the Prob That a point lies inside the sphere, lies outside the cube Solution Required probability favorable volume total volume a3 2 Clearly if edge length of cube is a radius of sphere will be

Ques: A sphere is circumscribed over a cube. Find the Prob That a point lies inside the sphere, lies outside the cube favorable volume total volume Solution Required probability a3 2 Clearly if edge length of cube is a radius of sphere il be Thus, volume of spher: 4 a33 2 2

Ques: A sphere is circumscribed over a cube. Find the Prob That a point lies inside the sphere, lies outside the cube favorable volume total volume Solution Required probability a3 2 Clearly if edge length of cube is a radius of sphere will be 4aV3 Thus, volume of sphere 32 2 2 Hence P-1--= 1- 7t 2

Given that xe [0. 1] and ye [O. 1]. LetA be the event of (x. y) satisfying y? s x and B be the event of (x. y) satisfying x3 sy. Then (A) P(A nB)-1 (C) A, B are mutually exclusive (B) A, B are exhaustive (D) A, B are independent

Given that xe [0. 1] and ye [O. 1]. LetA be the event of (x. y) satisfying y? s x and B be the event of (x. y) satisfying x3 sy. Then (A) P(A nB)-1 (C) A, B are mutually exclusive A the event of (x, y) belonging to the area OTQPO (B) A, B are exhaustive (D) A, B are independent Sol. B-the event of (x, y) belongint to the area OSQRO

Given that xe [0, 1] and ye [0, 1]. Let A be the event of (X. y) satisfying SX and B be the event of (x, y) satisfying x2 sy. Thern (A) P(An B) (C) A, B are mutually exclusive Athe event of (x, y) belonging to the area OTQPO (B) A, B are exhaustive (D) A, B are independent Sol. B the event of (x. y) belongint to the area OSQRO ar (OPORO) 1x1 3 ar (OPQRO)x 1 X

Given that xe [0. 1] and ye [O. 1]. LetA be the event of (x. y) satisfying y? s x and B be the event of (x. y) satisfying x3 sy. Then (A) P(A nB)-1 (C) A, B are mutually exclusive A the event of (x, y) belonging to the area OTOPO (B) A, B are exhaustive (D) A, B are independent Sol. B-the event of (x, y) belongint to the area osQRO dy dy2 1x1 3 w dx - P(A) = P(A) = ar(OTQPO)-1, ar(OPQRO 1 P(AnB).ari( POR L-Maried.2-1-1 RA) . P(B) = -=-P(An B). So, A and B are not independent RAoB) = 1, Pa: P(B)-3-3 # P(AoB). So A and B are not mutually exclusive.

unacademy Enroll Jagat Chaudhary Follow Qualified IIT-JEE,IT-JAM. Expert faculty for IIT-JEE Mathematics Courses. M.Sc. Ph.D. (MATHEMATICS) IIT Bhubaneswar Cofounder at Aspiration