MHT CET202519 Apr 2025Evening ShiftMathematicsProbabilityActual
If X B(n, p) then P(X=k) P(X=k-1) =
Options
- An - k k -1 p q
- Bn - k +1 k +1 p q
- Cn +1 k q p
- Dn - k +1 k p q
Correct answer
D. n - k +1 k p q
Step-by-step solution
For a binomial random variable X B(n, p) , the probability mass function is P(X=k) = n k p^k q^ n-k with q = 1 - p . The ratio P(X=k) P(X=k-1) can be expressed as n! k!(n-k)! p^k q^ n-k n! (k-1)!(n-k+1)! p^ k-1 q^ n-k+1 . Simplifying by canceling n! and applying exponent rules, the expression reduces to (k-1)!(n-k+1)! k!(n-k)! p q . Substituting k! = k (k-1)! and (n-k+1)! = (n-k+1) (n-k)! yields n-k+1 k p q . This corresponds to option D , confirming the final answer as D .