Question

One hundred identical coins, each with probability p of

showing up heads, are tossed once. If 0 < p < 1 and the

probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is –

• A. ½
• B. 49/101
• C. 50/101
• D. 51/101

Answer 1

Answer: (D)

51/101

Answer 2

Let X be the number of coins showing heads. Then X ~ B (100, p). We have

P (X = 51) = P (X = 50) Ž ¹⁰⁰C₅₁ p⁵¹ q⁴⁹ = ¹⁰⁰C₅₀ p⁵⁰ q⁵⁰ (where q = 1 – p)

Ž $\frac { p } { q }$ = $\frac { 100 ! } { 50 ! 50 ! }$ $\frac { 51 } { 50 }$

Ž 50p = 51 – 51p Ž 101p = 51.

Ž p = 51/101