There are two buckets containing same type of balls of different colours as below: Bucket A – Red 10%, White 60% and black 30% Bucket B Red 10%, White 40% and black 50%. If a white ball is drawn at random, what is the probability that it is from the bucket A?
Answers
Given : There are two buckets containing same type of balls of different colors as below:
Bucket A – Red 10%, White 60% and black 30%
Bucket B – Red 10%, White 40% and black 50%
To Find : The probability of selecting bucket A
The sample spaces for the above problem is
(c) If E is the event bucket 2 selected and F is the event white ball drawn. Then the value of P (F/E) is
If F is the event for white ball drawn then P(F) is
If white ball is drawn then the probability that it is drawn from 1st bucket is
Solution:
The probability of selecting bucket A = 1/2 as there are 2 buckets
The sample spaces for Selecting bucket is or ( 1 , 2)
The sample spaces for selecting ball
( 1 , R) , (1 , B) , (1 , W) , ( 2, R) , (2 , B) , (2 , W)
) If E is the event bucket 2 selected and F is the event white ball drawn. Then the value of P (F/E) is = 40/100 = 0.4
F is the event for white ball drawn then P(F) = (1/2) (60/100) + (1/2)(40/100)
= 0.5
white ball is drawn then the probability that it is drawn from 1st bucket is
White ball from bucket A = 0.6
White ball from bucket B = 0.4
= (0.6)/(0.6 + 0.4)
= 0.6
= 3/5
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