Question

Briana guesses at all 10 true/false questions on her history test. Find each probability.

P(at most half correct)

a.) 105/512 b.)319/512

Answer 1

Use niomial probability formula.

If there are only two possible outcomes, P and Q then there probabilities p and q add to one.
And (p+q)^n = 1

The probability of an event such that outcome P occurring r times in n trials is then
\[\left(\begin{matrix}n \\ r\end{matrix}\right) p^r q^{n-r}\]

P(at most half correct) is the same as saying you can have up to 5 correct, so you include the following: P(none correct) + P(1 correct) + P(2 correct)+...+P(5 correct)
The sum of these probabilities gives you your answer.