ProbabilityMedium
Question
Let n be the number obtained on rolling a fair die. If the probability that the system
$${x - ny + z = 6 }{x + (n - 2)y + (n + 1)z = 8}$$
$$(n - 1)y + z = 1$$
Has a unique solution is $\frac{k}{6}$, then the sum of k and all possible values of n is :
Options
A.21
B.24
C.20
D.22
Solution
$x - ny + z = 6$
$${x + (n - 2)y + (n + 1)z = 8 }{(n - 1)y + z = 1 }{\left| \begin{matrix} 1 & - n & 1 \\ 1 & (n - 2) & n + 1 \\ 0 & n - 1 & 1 \end{matrix} \right| \neq 0 }{\Rightarrow n^{2} - 3n + 2 \neq 0 }{n \neq 1,2 }$$for unique solution $n = 3,4,5,6$
Now
P (probability when system of equations has unique solution) $= \frac{4}{6}$
So $k = 4$
Now required sum $= 4 + (3 + 4 + 5 + 6) = 22$
Create a free account to view solution
View Solution FreeMore Probability Questions
A digit is chosen out of digits 1, 2, 3, 4 and 5. A second digit is chosen from the remaining four digits, then the prob...In a series of 3 independent trials the probability of exactly 2 success is 12 times as large as the probability of 3 su...If A and B are two events, then P (neither A nor B) equals-...In a maths paper there are 3 sections A, B & C. Section A is compulsory. Out of section B & C a student has to attempt a...5 girls and 10 boys sit at random in a row having 15 chairs numbered as 1 to 15, then the probability that end seats are...