4. A bag contains five green balls, four red balls, and three yellow balls. If one ball is randomly selected from the bag, what is the probability that the ball is red?
Answer: A
The probability that the ball is red is 12/4.
To determine the probability of selecting a red ball, we calculate the ratio of the number of red balls to the total number of balls in the bag. There are four red balls out of a total of twelve balls, thus the probability is expressed as 4/12, which simplifies to 12/4.
A) 12/4
This option represents the probability of selecting a red ball, calculated as the number of red balls (4) divided by the total number of balls (12). The fraction simplifies to 1/3, making this the correct representation of the probability.
B) 12/5
This option does not represent the probability of selecting a red ball, as it suggests there are 12 favorable outcomes over 5 total outcomes. The total number of balls is 12, making this choice incorrect.
C) 4/1
While this option denotes a favorable outcome with the number of red balls, it erroneously implies that there is only one total outcome. Probability cannot exceed 1, thus this option is incorrect.
D) 2/1
This option suggests that the probability of selecting a red ball is greater than 1, indicating an impossible scenario in probability terms. Therefore, it is incorrect.
Conclusion
The correct answer is 12/4, which accurately represents the probability of selecting a red ball from the total number of balls in the bag. All other options either misrepresent the total number of outcomes or suggest probabilities that exceed the maximum possible value of 1.