IBPS PO Reasoning: Probability questions with solutions

Q1. If the number of blue balls in bag C is more than 8 and the number of blue balls in bag C is more than the number of green balls in that bag, and the number of green balls in bag C is a prime number, which of the following statements is/are correct? I. The total number of red and blue balls in bag D can be equal to the number of blue balls in bag C. II. The probability of picking a blue ball from bag C is less than 0.75. III. The sum of the probability of picking a green ball from bag B and the probability of picking a blue ball from bag C is always greater than one.

1. Both (II) & (III)
2. Only (I)
3. All (I), (II) & (III)
4. Only (II)
5. Both (I) & (II)

Answer: Only (II)

Since blue balls in bag C are more than green balls and green is a prime number, the smallest possible configuration still keeps blue below three-fourths of the total only in certain cases, making statement II the only always-correct one. Statements I and III depend on unknown values from other bags and are not निश्चितly true.

Q2. The total number of balls in bag E is 25 and the probability of picking a blue ball from bag E is 0.2. The number of red balls in bag D is three times the number of blue balls in bag E. Find which of the following statements is/are correct. I. The difference between the number of blue balls in bag E and red balls in bag D is 9. II. The probability of picking a blue ball from bag D is less than \(\frac{1}{15}\). III. The probability of picking two red balls from bag D is \(\frac{7}{66}\).

1. Only I
2. Both I & II
3. Both II & III
4. Only III
5. None of these

Answer: None of these

Bag E has 25 balls and blue probability 0.2, so blue balls in E = 5. Red balls in D are three times that, so red balls in D = 15. The given statements do not all match these values, so the correct choice is none of these.