Probability Part 1

Let the coin is tossed ' n ' times.
Also, let x denote number of times head occurs.
According to the question,
P(X=7)=P(X=9)
Using formula P(X=r)=‌nCtptqn−r
where, p= probability of getting head in tossing a coin =1∕2 and q=1−p=1−1∕2=1∕2
∴P(X=7)=P(X=9)
⇒‌‌‌nC7(‌

1

2

)7(‌

1

2

)n−7=‌nC9(‌

1

2

)9(‌

1

2

)n−9
⇒‌‌‌nC7(‌

1

2

)n=‌nC9(‌

1

2

)n
⇒‌‌‌nC7=‌nC9
⇒n=7+9=16[∵‌nCr=‌nCq only when n=r+q]
∴‌‌P(X=2)=‌16C2(‌

1

2

)2(‌

1

2

)14
P(X=2)=‌

16!

2!14!

(‌

1

2

)16=‌

16×15

2

(‌

1

2

)16
=‌

23×15

216

=‌

15

213