instruction:
In this task, you need to provide the correct option for a given problem on probability from the provided options.
question:
Problem: in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turn on to be white , if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ? 
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 5 / 9 , d ) 3 / 7 , e ) 4 / 7
answer:
b


question:
Problem: the probability that event a occurs is 0.4 , and the probability that event b occurs is 0.45 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event b and event b will occur ? 
Options: a ) 0.25 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55
answer:
a


question:
Problem: how many positive integers less than 500 can be formed using the numbers 1 , 2,3 , and 5 for digits , each digit being used only once . 
Options: a ) 34 , b ) 677 , c ) 197 , d ) 177 , e ) 191
answer:

a