Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202622 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
22 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2026 · 22 January · Morning Shift · Mathematics · Probability

If a random variable x has the probability distribution array...

If a random variable xx has the probability distribution x01234567P(x)02kk3k2k22kk2+k7k2\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline P(x) & 0 & 2k & k & 3k & 2k^{2} & 2k & k^{2}+k & 7k^{2} \\ \hline \end{array}then P(3<x≤6)P(3 < x \leq 6) is equal to$

Options

  1. A0.64
  2. B0.22
  3. C0.33
  4. D0.34

Correct answer

C. 0.33

Step-by-step solution

Sum of all probabilities = 1
⇒0+2k+k+3k+2k2+2k+(k2+k)+7k2=1\Rightarrow 0 + 2k + k + 3k + 2k^2 + 2k + (k^2+k) + 7k^2 = 1
⇒10k2+9k−1=0\Rightarrow 10k^2 + 9k - 1 = 0.
⇒(10k−1)(k+1)=0\Rightarrow(10k-1)(k+1) = 0
⇒k=110\Rightarrow k = \frac{1}{10} (rejecting k=−1k = -1).
P(3<x≤6)=P(4)+P(5)+P(6)P(3 < x \le 6) = P(4) + P(5) + P(6)
=2k2+2k+k2+k= 2k^2 + 2k + k^2 + k
=3k2+3k=3(0.01)+3(0.1)=0.33= 3k^2 + 3k = 3(0.01) + 3(0.1) = 0.33.
Practice Probability on Quantrex Academy →

More from Probability

Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red… JEE Advanced 2026A candidate has to go to the examination centre to appear in an examination. The… JEE Main 2026A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement… JEE Main 2026A bag contains (N+1) coins - N fair coins, and one coin with 'Head' on both sides. A coin… JEE Main 2026The probabilities that players A and B of a team are selected for the captaincy for a… JEE Main 2026A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the… JEE Main 2026From a month of 31 days, 3 different dates are selected at random. If the probability… JEE Main 2026A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six… JEE Main 2026A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5… JEE Main 2026The probability distribution of a random variable X is given below : (array… JEE Main 2026A bag contains 10 balls out of which k are red and ( 10-k ) are black, where 0 ≤ k ≤ 10 .… JEE Main 2026Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of… JEE Main 2026From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one… JEE Main 2026Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls.… JEE Main 2026From the first 100 natural numbers, two numbers first a and then b are selected randomly… JEE Main 2026Two distinct numbers a and b are selected at random from 1,2,3, …, 50 . The probability… JEE Main 2026 Full Probability list Probability JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs