Question

Assuming that random guesses are made for ten multiple choice questions on an SAT, so there is n=10 trials, each with a probability of correct answers by p=0.2. That means each question has 5 choices with only 1 appropriate answer. Find the probability that the number if correct answers is exactly 6.

Answer 1

Okay, here we have this:

Here we are going to use the binomial probability equation to solve the problem, so we have the following formula:

Where:

n=total number of questions (trials)=10

k=number correct (successes)=6

n−k=number incorrect (failures)=4

p=probability of getting 1 question correct=(0.2)

q=1−p probability of getting 1 question incorrect=(0.8)

So we obtain the following:

`P=((n!)/(k!(n-k)!))p^kq^(n-k)`

Replacing:

`\begin{gathered} P=((10!)/(6!(10-6)!))0.2^6\cdot0.8^(10-4) \\ P=((10!)/(6!(4!)))0.2^6\cdot0.8^6 \\ P=((10\cdot9\cdot8\cdot7)/(4!))0.2^6\cdot0.8^6 \\ P=(5040)/(24)\cdot0.000064\cdot\: 0.262144 \\ P=(0.08455716864)/(24) \\ P=0.00352321536 \end{gathered}`