find the probability of guessing correctly at least 6 of the 10 answers on a true or false examination.

Question

the correct answer is 193/512

 

please explain and show all working. thanks very much! 

Answer 1

Simple trick:

 

Let N be the number of correct answers.

 

One of the following must hold: N ≤ 4 or N ≥ 6 or N = 5.

 

By symmetry,

 

P(N ≥ 6) = P(N ≤ 4) = [1 - P(N = 5)] / 2

 

So we compute C(10,5) = 10!/(5!5!) = 252

 

Therefore

 

P(N ≥ 6) = [1 - C(10,5) / 2¹⁰] / 2

 

= (1 - 252/1024) / 2

 

= 772/2048

 

= 193/512