Question

Maura guesses at all 10 questions on a true/false test. How do you find the probability that she got at least half correct?

Answer 1

`0.6230`

Explanation:

Let say p and q is a probability Maura guesses the answer. Since the answer is only true/false question, therefore,
`p=1/2, q = 1/2`

We use binomial theorem to solve where `X >=5`

`P(X>=5) = P(X=5)+P(X=6)+P(X=7) + P(X=8)+P(X=9)+P(X=10)`
`P(X>=5)=^10 C_5(1/2)^5(1/2)^5 + ^10 C_6(1/2)^6(1/2)^4 +^10 C_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(1/2)^0`

`P(X>=5)=252*(1/2)^10 + 210*(1/2)^10 + 120* (1/2)^10+ 45*(1/2)^10 + 10*(1/2)^10 + 1*(1/2)^10`

`P(X>=5)=(1/2)^10* (252+ 210+ 120+45+10 + 1)`

`P(X>=5)=(1/2)^10* (638)`

`P(X>=5) =0.6230`