Most Important Selected Qs for JEE AdvancedMathematicsProbability
Mr. A either walks to school or take bus to school everyday. The probability that he takes a bus to school is 1 / 4 . If he takes a bus, the probability that he will be late is 2 / 3 . If he walks to school, the probability that he will be late is 1 / 3 . The probability that Mr. A will be on time for at least one out of two consecutive days is p q , where p and q are co-prime, find the value of (q-p) .
Correct answer
25
Step-by-step solution
A: Mr. A reaches late B₁ : A goes to school by walking B₂ : A takes but to school E: A will be on time for atleast one out of 2 consecutive days. aligned P (B₁ ) & =3 / 4 P (B₂ ) & =1 / 4 P (A / B₁ ) & =1 / 3 P (A / B₂ ) & =2 / 3 P(A) & =P (B₁ A )+P (B₂ A ) & = 3 4 1 3 + 1 4 2 3 = 5 12 P P(E) & =1-P(A A)=1- 5 12 5 12 = 119 144 p q q-p & =144-119=25 aligned