Multiple choice

A bag is selected at random from two available bags. Bag 1 contains 6 red balls and 4 green balls, while Bag 2 contains 5 red balls and 5 green balls. The probability of selecting Bag 1 is 0.4, and the probability of selecting Bag 2 is 0.6. After selecting a bag, one ball is drawn at random from it. What is the probability that the ball drawn is red?

  1. 0.48

  2. 0.54

  3. 0.58

  4. 0.62

  5. a
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

P(Red) = P(Bag1)*P(Red|Bag1) + P(Bag2)*P(Red|Bag2) = 0.4 * (6/10) + 0.6 * (5/10) = 0.24 + 0.30 = 0.54.

AI explanation

Using the law of total probability, P(Red) = P(Bag 1) * P(Red|Bag 1) + P(Bag 2) * P(Red|Bag 2). The probability of drawing a red ball from Bag 1 is 6/10 and from Bag 2 is 5/10. Therefore, the total probability is (0.4 * 0.6) + (0.6 * 0.5) = 0.24 + 0.30 = 0.54.

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