CBSE Class 12-commerce Answered

Past records show that 80% of the operations performed by a certain doctor were successful . If he performs 4 operations per day what is the probability that at least 3 operations will be successful? Please give the solution to the following question posted on 8th March : The projection of a vector on the coordinate axes are 6,-3, 2 resp. Find its length and direction cosines. Also you had stated to give the answer to the second part of the second question posted on 8th March : Also find if the plane thus obtained contains the line x-2/3=y-1/1= z-2/5 Pls tell if you have answered this part of the question. Also pls refer your answer to my question posted on 3rd March : Find a unit vector in the XY plane which makes an angle of 45degree with vector i+j and 60 degree with the vector 3i-4j . You have stated in your answer that there is no such vector in the XY Plane. However there is such a vector as per answer given in the book and the vector is 1/14(13i +j). Hence I request you to please check the answer provided by you . Thanks

Asked by ahuja8087 | 10 Mar, 2017, 12:26: AM

Expert Answer

Dear student, the following are the solutions as we told you we shall provide. Hope this helps.

$begin mathsize 16px style Let space straight X space denote space the space number space of space successes space in space 4 space operations. Then comma space straight X space follows space binomial space distribution space with straight n equals 4 straight p equals successful space operation equals 80 over 100 equals 4 over 5 straight q equals failed space operation equals 20 over 100 equals 1 fifth straight P left parenthesis at space least space 3 space operations space are space successful right parenthesis equals straight P left parenthesis straight X greater or equal than 3 right parenthesis equals straight P left parenthesis straight X equals 3 right parenthesis plus straight P left parenthesis straight x equals 4 right parenthesis space equals straight C presuperscript 4 subscript 3 open parentheses 4 over 5 close parentheses cubed open parentheses 1 fifth close parentheses to the power of 1 plus straight C presuperscript 4 subscript 4 open parentheses 4 over 5 close parentheses to the power of 4 open parentheses 1 fifth close parentheses to the power of 0 equals 4 cross times open parentheses 4 over 5 close parentheses cubed cross times open parentheses 1 fifth close parentheses plus 1 cross times open parentheses 4 over 5 close parentheses to the power of 4 cross times 1 equals open parentheses 4 over 5 close parentheses cubed open square brackets 4 over 5 plus 4 over 5 close square brackets equals 64 over 125 cross times 8 over 5 equals 512 over 625 end style$