Question

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to that of getting 9 heads, the probability of getting 2 heads is -

• A. $\frac { 15 } { 2 ^ { 12 } }$
• B. $\frac { 15 } { 2 ^ { 13 } }$
• C. $\frac { 35 } { 2 ^ { 12 } }$
• D. $\frac { 2 } { 15 }$

Answer 1

Answer: (C)

$\frac { 35 } { 2 ^ { 12 } }$

Answer 2

Let a coin is tossed 'n' times

\ ${ } ^ { \mathrm { n } } \mathrm { C } _ { 6 }$ . $\left( \frac { 1 } { 2 } \right) ^ { n }$ = ${ } ^ { \mathrm { n } } \mathrm { C } _ { 10 }$ $\left( \frac { 1 } { 2 } \right) ^ { n }$ ̃ n= 16

Required probability = ${ } ^ { 16 } C _ { 3 }$ $\left( \frac { 1 } { 2 } \right) ^ { 3 }$ . $\left( \frac { 1 } { 2 } \right) ^ { 13 }$

= $\frac { 16 \times 15 \times 14 } { 6 } \times \frac { 1 } { 2 ^ { 16 } }$ = $\frac { 35 } { 2 ^ { 12 } }$