Answer to Question #180708 in Statistics and Probability for phemelo mongae

Question

A true-false test is given for five questions. To pass, you need at least four (4) questions to be correct. If you guess each answer, what is the probability that you’d pass the test? 

Answer 1

Since In true false question, There are 50% chance of true and vice versa,

$p=0.5,q=1-p=0.5\\n=5$

Probability of Passing the test $=P(X\ge 4)=P(X=4)+P(X=5)$

$=^5C_4(0.5)^4(0.5)+^5C_5(0.5)^5$

$=6\times(0.5)^5=0.1875$