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Three bags, labeled X₁, X₂, and X₃, contain balls of different colors. Bag X₁ has 5 red and 5 green balls, X₂ has 3 red and 5 green balls, and X₃ has 5 red and 3 green balls. The probabilities of selecting bags X₁, X₂, and X₃ are 3/10, 3/10, and 4/10, respectively. If a bag is randomly selected and a ball is drawn from it, which of the following statements is accurate?
- The likelihood that bag X₃ was chosen, given that the ball drawn is green, is 5/13.
- The probability of drawing a green ball, assuming bag X₃ was chosen, is 3/8.
- The chance of selecting bag X₃ and drawing a green ball is 3/10.
- The overall probability of drawing a green ball is 39/80.
Correct answer: The probability of drawing a green ball, assuming bag X₃ was chosen, is 3/8.
Solution
The probability of drawing a green ball from bag X₃ is calculated as the ratio of green balls to total balls in X₃, which is 3/8. This matches the correct statement.
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