Multiple choice

There are two bags A and B. Bag A contains 6 red balls and 10 green balls and Bag B contains 4 red balls and 6 green balls. One bag is selected at random. From the selected bag one ball is drawn at random. What is the probability that the ball drawn is red?

  1. 27/80

  2. 31/80

  3. 39/80

  4. 29/80

  5. 33/80
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Probability of selecting Bag A = 1/2, Bag B = 1/2. If Bag A chosen: P(red) = 6/16 = 3/8. If Bag B chosen: P(red) = 4/10 = 2/5. Total P(red) = (1/2 × 3/8) + (1/2 × 2/5) = 3/16 + 1/5 = 15/80 + 16/80 = 31/80. This uses the law of total probability for mutually exclusive events.

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