Question

A student guesses the answers to 6 questions on a true-false quiz. Find the probability that the indicated number of guesses are correct:

fewer than 5 (Hint: Fewer than 5 means exactly 0 or exactly 1 or exactly 2 or exactly 3 or exactly 4.)

a.≈0.96

b.≈0.67

c.≈0.74

d.≈0.89

how do i solve this?

Answer 1

The probability of getting a question correct is 0.5
If we find the probabilities of getting 5 correct and 6 correct, add these two probabilities and subtract the result from 1.0000 we will have the required probability that fewer than 5 guesses are correct.
The binomial distribution applies:
\[P(5\ correct)=\left(\begin{matrix}6 \\ 5\end{matrix}\right)0.5^{5}0.5^{1}=0.109375\]

Answer 2

\[P(6\ correct)=\left(\begin{matrix}6 \\ 6\end{matrix}\right)0.5^{6}0.5^{0}=0.015625\]
P(5 correct) + (P6 correct) = 0.109375
P(fewer than 5 correct) = 1.000000 - 0.109375 = ?