Question

A fair coin is tossed a fixed number of times. If the probability of getting 6 heads is equal to that of getting 8 tails

then the probability of getting 2 heads, is -

• A. 91/41⁴
• B. 91/4⁷
• C. 18²/4⁷
• D. 18²/41⁴

Answer 1

Answer: (B)

91/4⁷

Answer 2

Let the coin is tossed n times. If x denote the number of times head occurs

P ( x = 6) = P ( x = n – 8)

ŽⁿC₆$\left( \frac { 1 } { 2 } \right) ^ { 6 } \left( \frac { 1 } { 2 } \right) ^ { \mathrm { n } - 6 }$=

Ž n = 8 + 6 Ž n = 14

Hence P (x = 2) = $\frac { 14.13 } { 2 ^ { 15 } }$ = $\frac { 91 } { 4 ^ { 7 } }$