Dr. Brajesh Kumar Jha

B.Tech Probability Questions with Detailed Solutions Topic: Simple / Classical Probability Level: B.Tech Engineering Mathematics Marks: 6-10 Marks Each Question 1: Probability Based on Playing Cards A card is drawn at random from a well-shuffled standard deck of 52 playing cards. Find the probability that the card drawn is: a king or a queen, a red face card, neither an ace nor a king, either a heart or a face card. Show Detailed Solution Total number of cards in a standard deck: \( n(S) = 52 \) The classical definition of probability is: \[ P(E)=\frac{\text{Number of favourable outcomes}} {\text{Total number of equally likely outcomes}} \] (a) Probability of drawing a King or Queen Number of kings = 4 Number of queens = 4 Therefore, ...

Return to Table of Content   Successive Differentiation Let   be a function of   the derivative or Differential coefficient of   w.r.t.   is denoted by Where   Similarly the second order derivative of y w.r.t. x is defined as Similarly we get nth derivative or Differential coefficient of   w.r.t.   and is denoted by   Application: 1.     Series expansion of a function like Taylor’s and McLaurin's series expansion. 2. Solution of ordinary and partial differential equations. Ex. Using Taylor’s Series Example 1: Find the nth derivative of Solution: differentiating y w.r.t. x we get,           …….......(1) Differentiating again w.r.t. x, we get …….......(2) Similarly differentiating successively, we get              …….......(3) .......(4) …   …   …   …   … ...