Explanation
Solution
Step 1: Probability define karein.
Ek dice roll karne par odd number aane ki probability p aur even number aane ki probability q dono barabar hoti hain:
Step 2: Binomial Distribution ka use karke n ki value nikaalein.
Humein diya gaya hai ki P(X=7)=P(X=9), jahan X odd numbers ki sankhya hai:
Chunki p=q=21, toh p7qn−7=(21)n aur p9qn−9=(21)n dono barabar hain. Isliye:
Combinations ki property (xn)=(yn)⟹x+y=n ka use karne par:
Step 3: Even numbers aane ki probability nikaalein.
Ab humein probability nikaalni hai ki even number "twice" (do baar) aaye:
P(Even=2)=(216)(21)2(21)14
P(Even=2)=(216)(21)16=216(216)
Step 4: k ki value calculate karein.
(216) ki value calculate karte hain:
Toh probability hogi:
Sawal ke anusar ye probability 215k ke barabar hai:
