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I'm not sure how they are getting 5/16 as the answer.

The question is:

Suppose you take a true/false quiz consisting of four questions, each worth 25%. If a score of 50% or less fails the quiz, what is the probabillity that you can pass the quiz by randomly guessing each answer?

Well here is how I broke it down...

If you get a 50% or less you fail, so you need at least 3 out of the 4 right to get a 75%.

I then thought, how many possible outcomes are there? Well its like tossing a coin, its either Head or Tails or in this case True or False so you have:

2^4 = 16 possible outcomes.

Now I thought to use combinations, you want 4 choose 3,

Step 1: Choose first question (T or F)

Step 2: Choose 2nd question (T or F)

Step 3: choose 3rd qustion (T or F)

Step 4: choose 4th question (T or F)

but I soon realized I dont' think i can apply the multiplication rule on this, there are too many cases so i tried combinations and i said:

4 choose 3 = 4. So the probabily i said was:

4/16 = 1/4.

But the answer is 5/16.

ANy ideas?