A bag contains 6 red balls and 10 green balls. Another bag contains 4 red balls and 6 Green balls. A bag is picked up at random and one ball is picked up. What is Probability that picked up ball is Red?
How to calculate pick a ball Probability for Two bags?
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probability
probability-theory
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2You need to tell us what you know or have tried, and where you are stuck. – 2017-01-17
2 Answers
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If bag 1 is chosen, the probability of a randomly picked ball is red is $6/16 = 3/8$ (for 6 out of its 16 balls are red). For bag 2, this is $4/10 = 2/5$. Then if each bag is chosen with probability $1/2$, The probability you're looking for is $$ \Pr(\text{chosen ball is red}) = \Pr(\text{bag 1 is chosen}) \Pr (\text{random ball from bag 1 is red})+\Pr(\text{bag 2 is chosen}) \Pr (\text{random ball from bag 2 is red}) = \frac{1}{2} \times \frac{3}{8} + \frac{1}{2} \times \frac{2}{5} = \frac{31}{80} $$
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HINT: If you can solve the problem for each bag, then just take the average.