The probability of guessing correctly atleast 8 out of 10 answers on a true falsetype examination is

Options

A. `7/64`
B. `7/128`
C. `45/1024`
D. `7/41`

Explanation

we know that, P(X=r)=`""^(n)C_(r)(p)^(r )(q)^(n-r)`
Here, `n=10,p=1/2,q=1/2`
and `rge8 i.e.,r=8,9,10`
`rArrP(X=r)=P(r=8)+P(r=9)+P(r=10)`
`=""^(10)C_(8)(1/2)^(8)(1/2)^(10-8)+""^(10)C_(9)(1/2)^(9)(1/2)+""^(10)C_(10)(1/2)^(10)(1/2)^(0)`
`=(10!)/(8!2!)(1/2)^(10)+(10!)/(9!1!)(1/2)^(10)+(1/2)^(10)`
`=(1/2)^(10)cdot[45+10+1]=(1/2)^(10)cdot56`
`=1/(16cdot64)cdot56=7/128`