Multiple choice

State the correct relationship between Q I, Q II and Q III Q I : A bag contains 50 balls which are pink, violet and red .Find the number of violet balls in the bag, if probability of picking pink ball is 3/5 and that of either a pink or violet ball is 4/5. Q II : A bag contains 40 balls pink, violet and red. The probability of picking violet ball is 3/8. If the first ball was violet and without replacement, probability of picking a pink ball is 4/13.Find the number of red balls. Q III : There are 5 Red balls, 4 Yellow balls and 3 black balls in a bag. Four balls are chosen at random. The probability of their being 2 Red and 2 Yellow ball.

  1. Q I > Q II > Q III

  2. Q I < Q II < Q III

  3. Q I = Q II = Q III

  4. Q III < Q I < Q II

  5. Q I = Q II > Q III
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D Correct answer
Explanation

Q I: P(pink)=3/5 so pink=30. P(pink or violet)=4/5 so pink+violet=40, thus violet=10. Q II: P(violet)=3/8, violet=15. After removing violet: 39 balls left, P(pink)=4/13 so pink=12. Red=40-15-12=13. Q III: Total=12. P(2 red from 5)*P(2 yellow from 4) = C(5,2)*C(4,2)/C(12,4) = 10*6/495=60/495=4/33 ≈ 0.121. 10 < 13 < 0.121 is meaningless - Q III is probability, not count. Comparing as values: 10 < 13, and 4/33 ≈ 0.12. So Q I=10, Q II=13, Q III≈0.12. Order: Q III < Q I < Q II.

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