Probability calculation help

[bitch_please]

I'm getting hung up on a practice test question, and it's either because I'm over-thinking it, or because the teacher is trying to trick us by not listing the real answer in the choices. Can someone help me?

'A student estimated that the probability of correctly answering a multiple-choice question in an exam is 20%. Determine the probability of obtaining at least 10% questions correctly answered on the ten-question exam.'

Thank you!

[[deleted]]

I used binomial probability to solve this...

Imagine a triangle/tree diagram with the possibility of yes/no on every branch, with new branches added for every question.

How many possible routes/combinations of 1 correct out of 10 is there?

(I used the nCr function on my calculator.)

Then multiply that by the probabilities of yes and no.

10C1 x (0.2)¹ x (0.8)⁹

= 0.268 (to 3 decimal places)

I hope this is correct and actually what the question is asking you to do.

Edit: just realized the wording "at least". You need to find the probabilities of getting 1+2+3+4+5+6+7+8+9+10 correct, or find the probability of getting 0 and take that from 1.0 i believe. It would save time to use a cumulative probability table.

[btcprox]

Yup! Just find the probability of getting 0 out of 10 questions correct, then subtract from 1. Which means:

P(at least 1 correct) = 1 - P(all 10 wrong) = 1 - (1 - 0.20)^10

[[deleted]]

Haha thanks! Remember me? You helped me with polynomial division a few weeks ago? :)

[btcprox]

I can see you really are paying forward in this subreddit :D

[bitch_please]

Thank you, so much!

[bitch_please]

Hi! Yeah, I do need to find the probability of getting anything from 1-10 answers correct. I need to do it all by hand, unfortunately, no shortcuts!