MHTCET 2016 Math Solved Paper

(a) In every true and false question, probability of guessing correctly, p =

1

2

and probability of guessing wrongly, q =

1

2

Here, n = 10
The probability of atleast 7 correctly guessing
= P(X > 7)
= P(X = 7) + P(X = S) + P(X = 9)+ P(X = 10)
=10C7(

1

2

)7(

1

2

)3 + 10C8(

1

2

)8(

1

2

)2 + 10C9(

1

2

)9(

1

2

)1 + 10C10(

1

2

)10
[∵P(x=r)=nCrprqn−r]
=120(

1

2

)10 + 45(

1

2

)10 + 10(

1

2

)10 + 1(

1

2

)10
=

120+45+10+1

210

=

176

1024

=

11

64