Statistics Worksheet With Answers - Stat 200 (Page 3 of 6) in pdf

Statistics Worksheet With Answers - Stat 200 Page 3

On a standard SAT test, a typical question has five possible answers; A, B, C, D, and E. Only

one answer is correct. If you guess you have a 1 out of 5 or 20% chance of being correct.

What is the probability of not being correct on a question if you randomly guess?

This is the complement of guessing correctly

P(not correct) = 1-.20 = .80

What is the probability of being correct on three questions if you you randomly guess?

Assume independence between questions

P(3 right) = .2*.2*.2 = .008

What is the probability of getting at least one question right on three questions if you

randomly guess?

At least one right means the P(3 right)+ P(2 right)+P(1 right)

P(3 right) = .2*.2*.2 = .008

P(2 right) = (.2*.2*.8)*3 = .096

P(1 right) = (.2*.8*.8)*3 = .384

So, P(at least 1 right) = .008+.096+.384 = .488

In other words, 1-P(none right)

1 - (.8*.8*.8) = 1-.512 = .488

What is the probability of getting all three questions wrong on three questions if you

randomly guess?

P(all 3 wrong) = .8*.8*.8 = .512

Training on how to do better on the SAT test advise that you should guess if you can

eliminate possible answers. Suppose on a question you can eliminate two possible

answers. What is the probability that you are right if you randomly guess your answer

on the remaining items.

This is a Conditional Probability: the probability of a correct guess given you eliminate two

answers.

Now we have a 1/3 = .333 chance of guessing the answer correctly.

Statistics Worksheet With Answers - Stat 200 Page 3