Question

The probability that a student guesses the correct answer to a five​-choice multiple choice question is ​P(correct)equals0.2. How many correct answers should a student expect to guess on a test with 70 five​-choice multiple choice​ questions?

Answer 1

For each question we have 4 choices. So if you have 10 on such questions, you ll have :

4*4*4*4*4*4*4*4*4*4= 4^10 = 2048

Getting 8 correct means=> 8 corrects and two wrongs

3/4 is the probability if a question is answered wrong

1/4 is the probability if a question is answered correctly

so we can consider this probability :

P=(3/4)*(3/4)*(1/4)*(1/4)*(1/4)*(1/4)*(1/4)*(1/4)*(1/4)*(1/4)

=> P=0.00000858306

But as we can select any combination of 2 from 10 for being wrong, so we need to multiply P by (10,2)=10!/(2!*8!) =45

so the answer is P*45 = 0.00038623809

So not very lucky to answer randomly!

By the way, is it a question from your home work assignment? ;) ;

tbh google