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For each question, there is a 1/2 chance at getting the question correct by guessing.
Let's take a scenario to better understand.
Suppose the true-false paper has 5 questions. For a perfect score by guessing, you'd need to get all 5 correct (ie (1/2)⁵)
The reason why you multiply is because you need each 1/2 simultaneously for a perfect score, which is an important concept when doing binomial probability later on.
Thus, let's use this knowledge to answer the question.
We need the minimum amount of questions such that the probability is less than 1/10.
We can write an inequality for this:
Now, we need to log both sides to find n.
n > 3.3219...
n ≈ 4
Thus, 4 questions is the minimum number of questions needed.
Let's take a scenario to better understand.
Suppose the true-false paper has 5 questions. For a perfect score by guessing, you'd need to get all 5 correct (ie (1/2)⁵)
The reason why you multiply is because you need each 1/2 simultaneously for a perfect score, which is an important concept when doing binomial probability later on.
Thus, let's use this knowledge to answer the question.
We need the minimum amount of questions such that the probability is less than 1/10.
We can write an inequality for this:
Now, we need to log both sides to find n.
n > 3.3219...
n ≈ 4
Thus, 4 questions is the minimum number of questions needed.
Since they are simmilar we will then have the following relationships.
Now, we solve for x, as follows:
The expression goes along the lines of. 15 is to 10 what 9 is to x, with this as was done we solve for x and determine it's value, that since they keep proportionality.