Four numbers are chosen at random (without replacement) from the set \(\{1, 2, 3, \ldots, 20\}\).Statement 1: The probability that the chosen numbers when arranged in some order will form an A.P. is 1/85.Statement 2: If the four chosen numbers form an A.P., then the set of all possible values of common difference is \(\{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5\}\).
For Problems 7–9: A JEE aspirant estimates that she will be successful with an 80% chance if she studies 10 hours per day, with a 60% chance if she studies 7 hours per day, and with a 40% chance if she studies 4 hours per day. She further believes that she will study 10 hours, 7 hours, and 4 hours per day with probabilities 0.1, 0.2, and 0.7, respectively.The chance she will be successful is
NTA Test 16 (Numerical)
If $a_1, a_2, b_1$ and $b_j$ take values in the set $\{1, -1, 0\}$, then the probability that the equation $a_1x + b_1y = 0$ satisfies $\frac{c}{p}$ (p & q are co-prime) then, $q - 2p$ is
For Problems 7–9: A JEE aspirant estimates that she will be successful with an 80% chance if she studies 10 hours per day, with a 60% chance if she studies 7 hours per day, and with a 40% chance if she studies 4 hours per day. She further believes that she will study 10 hours, 7 hours, and 4 hours per day with probabilities 0.1, 0.2, and 0.7, respectively.Given that she does not achieve success, the chance she studied for 4 hours is
A doctor is called to see a sick child. The doctor knows (prior to the visit) that 90% of the sick children in that neighbourhood are sick with the flue, denoted by F, while 10% are sick with the measles, denoted by M. The probability of having a rash for a child sick with the measles is 0.95. However, occasionally children with the flue also develop a rash with conditional probability 0.08. Upon examination the child, the doctor finds a rash, then the probability that the child has the measles, is
A student appears for tests I, II, and III. The student is successful if he passes either in tests I and II or tests I and III. The probabilities of the student passing in tests I, II, and III are, respectively, \(p\), \(q\), and 1/2. If the probability that the student is successful is 1/2, then \(p(1 + q) =\)
The coefficients $a,b,c$ in the quadratic equation $ax^2+bx+c=0$ are chosen from the set $\{1,2,3,4,5,6,7,8\}$. The probability of this equation having repeated roots is:
All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number n be denoted by W . Let the probability P (W ) of choosing the n n word W satisfy P (W$) = 2P$(W n n$n-1$) ,$n > 1$.$\alpha$If$P(CDBEA) = 2$$\beta$,$\alpha$,$\beta$$\ in $N , then$\alpha$+$\beta$is equal to : _______$2 -1$
Three distinct numbers are selected randomly from the set {1, 2, 3,$\ldots$$\ldots$, 40}. If the probability, that the selected numbers are in an increasing G.P. is m n , gcd(m,$n) = 1$, then$m + n$is equal to _____.