In: Statistics and Probability
We have 3 boxes. Box A contains 1 yellow ball and 2 red balls. Box B conatins 2 yellow balls and 2 red balls. Box C contains 2 yellow balls and 1 red ball. First, we randomly choose between Box A and Box B. Then we randomly choose a ball from the selected box and put the ball into Box C. Lastly, we randomly choose a ball from Box C.
Let E1 be the event that Box A is chosen first. Let E2 be the event that the first ball chosen is red. Let E3 be the event that the last ball chosen is red.
Find P(E2)
First we obtain all the possibilities here for the experiment as:
From the above situations, there are 4 out of 8 cases, when E2
is happening. Therefore the probability here is computed as:
P(E2) = (1/6) + (1/8) + (1/6) + (1/8) = 1/3 + 1/4 = 7/12
Therefore 7/12 is the required probability here.