JEE Main202224 Jun 2022Evening ShiftMathematicsProbabilityActual
A random variable X has the following probability distribution: X 0 1 2 3 4 P X k 2 k 4 k 6 k 8 k The value of P 1 < x < 4 x ≤ 2 is equal to
Options
- A4 7
- B2 3
- C3 7
- D4 5
Correct answer
A. 4 7
Step-by-step solution
To find P 1 < x < 4 x ≤ 2 or P A B We know that P A B = P A ∩ B P B Given x 0 1 2 3 4 P x k 2 k 4 k 6 k 8 k P A = 2 , 3 P B = 0 , 1 , 2 P A ∩ B = P x = 2 P B = P x = 0 + P x = 1 + P x = 2 So    P A B = P x = 2 P x = 0 + P x = 1 + P x = 2 = 4 k k + 2 k + 4 k = 4 k 7 k = 4 7 Hence option A is correct.