Probability of guessing correctly atleast 7 out of 10 answers in a 'True' or 'False' test is equal to

Options

A. `(11)/(64)`
B. `(11)/(32`
C. `(11)/(16)`
D. `(27)/(32)`

Answer

A

Explanation

In each true and false question, prbability of guessing correctly is `p=(1)/(2)` and probability of not guessing correctly `q=(1)/(2)`
Here, n=10
`thererfore` The probability of guessing atleast 7 correctly `=P(X ge 7)`
`=P(X=7)+P(X=8)+P(X=9)+P(X=10)`
`""10C_(7) ((1)/(2))^(7) ((1)/(2))^(3)+""^(10)c_(8) ((1)/(2))^(8) ((1)/(2))^(2)+""^(10)c_(9) ((1)/(2))^(9) ((1)/(2))^(1)+""^(10)C_(10) ((1)/(2))^(10)` `[therefore P(x=r)=""^(n)C_(r)p^(r)q^(n-r)]`
`120xx((1)/(2))^(10)+45((1)/(2))^(10)+10((1)/(2))^(10)+1((1)/(2))^(10)`
`=(120+45+10+1)/(2^(10))=(176)/(1024)=(11)/(64)`