JEE Main20238 Apr 2023Evening ShiftMathematicsProbabilityActual
If the probability that the random variable X takes values x is given by P ( X = x ) = k ( x + 1 ) 3 - x , x = 0 , 1 , 2 , 3 , … … , where k is a constant, then P ( X ≥ 2 ) is equal to
Options
- A7 27
- B7 18
- C11 18
- D20 27
Correct answer
A. 7 27
Step-by-step solution
Given, The probability that the random variable X takes values x is given by P ( X = x ) = k ( x + 1 ) 3 - x , x = 0 , 1 , 2 , 3 , … … , where k is a constant, Now we know that, P ( X = 0 ) + P ( x = 1 ) + P ( x = 2 ) + … … … = 1 ⇒ k 3 0 + 2 k 3 1 + 3 k 3 2 + … . . = 1 ⇒ k 1 + 2 3 + 3 3 2 + … . = 1 Now finding, S = 1 + 2 3 + 3 3 2 + 4 3 3 + …     . . . . 1 ⇒ S 3 = 1 3 + 2 3 2 + 3 3 2 + … …     . . . . . 2 Now on subtra