A student takes a true/false quiz with four questions, each equally likely to be

Question

A student takes a true/false quiz with four questions, each equally likely to be either T or F.
1. What is the probability of getting question 1 correct?
2. What is the probability of getting exactly one question wrong?
3. What is the probability of getting three or more questions correct?
4. What is the probability of getting the first two questions correct?
5. What is the probability of getting all four questions correct given that the answers to the first two questions are correct?

Please explain each in detail. Thank you

Explanation / Answer

1. Since there are 2 possible answers and one correct answer, the probability of getting question 1 correct is 1/2, also written .5 or 50%.
2.I'm going to use nCr=n!/(n-r)!r! for this.The equation for this is .54*(4!/3!1!). You could use this to find either exactly one wrong or exactly one right out of the 4 questions. So, the probability of getting exactly one wrong is (0.0625)(24/6)=0.25.

3. We'll do the same to find the probability of getting exactly 3 questions correct and exactly 4 questions correct. .54*(4!/1!3!)=(0.0625)(24/6)=0.25. .54*1=0.0625. (note- if n and r are the same, it equals 1) Add these two together to get the answer to question 3, which equals 0.3125.

4. For this one we use nPr=n!/(n-r)!, it is pretty much like nCr except order matters now. So, .54*(4!/2!)=(0.0625)(24/2)=0.75.

5. We use what we got for number 4 (0.75) and add .54*1 to it. (I used nCr, or 2C2 because order doesn't matter now and you have to find the probability of getting 2 out of the last 2 questions right) So, 0.75+0.0625=0.8125.

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