Multiple choice

A bag X contains 4 white and 2 black balls.Another bag Y contains 3 white and 4 black balls.A bag is selected at random and a ball is drawnat random from it. I. the probability that the ball drawn is white is $\frac{17}{42}$. II. The probability that the ball drawn is black is $\frac{19}{42}$. Which of the above statements is correct

  1. only I

  2. only II

  3. both I and II

  4. neither I nor II
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

P(W) = P(Bag X)P(W|X) + P(Bag Y)P(W|Y) = 0.5 * (4/6) + 0.5 * (3/7) = 1/3 + 3/14 = (14+9)/42 = 23/42. P(B) = 1 - P(W) = 1 - 23/42 = 19/42. Statement II is correct.

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