Correct Option (3)
To determine the probability of winning, we first calculate the total number of balls and the number of balls that satisfy the winning conditions.
- Total number of red balls = 15
- Total number of black balls = 20
- Total number of balls in the bag = 15 + 20 = 35
The winning conditions are:
- The ball is red and numbered 3.
- The ball is black and numbered 1 or 2.
Calculating the number of balls for each winning condition:
- Number of red balls numbered 3: 40% of 15 = (40/100) * 15 = 6 balls.
- Number of black balls numbered 1: Among black balls, 45% are numbered 2 and 30% are numbered 3. Therefore, the percentage of black balls numbered 1 is 100% - 45% - 30% = 25%. Number of black balls numbered 1 = 25% of 20 = (25/100) * 20 = 5 balls.
- Number of black balls numbered 2: 45% of 20 = (45/100) * 20 = 9 balls.
Total number of black balls numbered 1 or 2 = 5 (numbered 1) + 9 (numbered 2) = 14 balls.
Total number of favorable outcomes (winning balls) = (Red balls numbered 3) + (Black balls numbered 1 or 2) = 6 + 14 = 20 balls.
The probability of winning is calculated as the ratio of favorable outcomes to the total number of balls:
Probability of winning = (Favorable outcomes) / (Total balls) = 20 / 35 = 4 / 7.
Incorrect Options:
The other options represent numerical values that do not align with the calculated probability of 4/7. These options are arithmetically incorrect based on the given conditions and the principles of probability calculation.
