Explanation
1. Set up the Equation:
According to the question, P(X=50)=P(X=51).
100C50⋅P50⋅(1−P)100−50=100C51⋅P51⋅(1−P)100−51
100C50⋅P50⋅(1−P)50=100C51⋅P51⋅(1−P)49
2. Simplify the Terms:
Divide both sides by P50 and (1−P)49:
3. Expand the Combinations:
50!⋅50!100!⋅(1−P)=51!⋅49!100!⋅P
Cancel 100! from both sides and expand the factorials (51!=51⋅50! and 50!=50⋅49!):
50⋅49!⋅50!1⋅(1−P)=51⋅50!⋅49!1⋅P
Cancel 49! and 50! from the denominators:
4. Solve for P:
Cross-multiply:
Conclusion:
The value of P is 10151.
Correct Option: (d)
