Probability challenge 3
A bag contains 5 balls all of different colors (one of which is white). Three people and whose probabilities of speaking truth are and , respectively, assert that a ball drawn from the bag is white. What is the probability of truth of their assertion?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
P(white drawn & reported | white reported)
= {(1/5)[(1/2)(1/1)][(2/3)(1/1)][(3/4)(1/1)]} / {(1/5)[(1/2)(1/1)][(2/3)(1/1)][(3/4)(1/1)] +
(4/5)[(1/2)(1/4)][(1/3)(1/4)][(1/4)(1/4)]}
= { 1 / 20 } / { 1 / 20 + 1 / 1920 }
= 96 / 97