Let, X denote the number of colleges where you will apply after your results and P(X = x) denotes your probability of getting admission in x number of colleges. It is given thatPX = x = kx,if x = 0 or 12 kx,if x = 2k5-x,if x = 3 or 40,if x > 4where k is a positive constant. Find the value of k. Also find the probability that you will get admission in (i) exactly one college (ii) at most 2 colleges (iii) at least 2 colleges.

Let, X denote the number of colleges where you will apply after your r

1.	Let, X denote the number of colleges where you will apply after your results and P(X = x) denotes your probability of getting admission in x number of colleges. It is given thatPX = x = kx,if x = 0 or 12 kx,if x = 2k5-x,if x = 3 or 40,if x > 4where k is a positive constant. Find the value of k. Also find the probability that you will get admission in (i) exactly one college (ii) at most 2 colleges (iii) at least 2 colleges.
Answer» Let, X denote the number of colleges where you will apply after your results and P(X = x) denotes your probability of getting admission in x number of colleges. It is given that $P (X = x) = \{\begin{cases} k x & , & if x = 0 or 1 \\ 2 k x & , & if x = 2 \\ k (5 - x) & , & if x = 3 or 4 \\ 0 & , & if x > 4 \end{cases}$ where k is a positive constant. Find the value of k. Also find the probability that you will get admission in (i) exactly one college (ii) at most 2 colleges (iii) at least 2 colleges.