Multiple choice general knowledge science & technology

There are 2 bags. The 1st bag contains 3 RED and 2 BLACK ball. The 2nd bag contains 4 RED and 6 BLACK ball. if a man choses a bag at random and picks a ball then what is the probability that the ball is RED?

  1. 7/15

  2. 1/2

  3. 1/3

  4. 8/15
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is total probability theorem. P(Red) = P(choose bag 1) × P(Red|bag 1) + P(choose bag 2) × P(Red|bag 2) = (1/2) × (3/5) + (1/2) × (4/10) = 3/10 + 2/10 = 5/10 = 1/2. Each bag is equally likely to be chosen, then we combine the weighted probabilities.

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