A bag contains five green balls, four red balls, and three yellow balls. If one ball is randomly selected from the ball, which of the following is the probability that the ball is red?
A.
5/12
B.
¼
C.
½
D.
1/3
The correct answer and Explanation is :
To solve this problem, we need to calculate the probability of selecting a red ball from a bag containing green, red, and yellow balls.
Step 1: Determine the total number of balls.
- The bag contains:
- 5 green balls,
- 4 red balls, and
- 3 yellow balls.
The total number of balls in the bag is:
[
5 \, \text{(green)} + 4 \, \text{(red)} + 3 \, \text{(yellow)} = 12 \, \text{balls}.
]
Step 2: Determine the number of favorable outcomes.
- The favorable outcome here is selecting a red ball. Since there are 4 red balls in the bag, there are 4 favorable outcomes.
Step 3: Calculate the probability.
The probability of an event is given by the formula:
[
\text{Probability of an event} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}.
]
In this case, the probability of selecting a red ball is:
[
\text{P(red)} = \frac{4 \, \text{(favorable outcomes)}}{12 \, \text{(total outcomes)}} = \frac{4}{12}.
]
Step 4: Simplify the fraction.
[
\frac{4}{12} = \frac{1}{3}.
]
Thus, the probability of selecting a red ball is (\frac{1}{3}).
Conclusion:
The correct answer is D. ( \frac{1}{3} ).
Explanation:
There are 12 total balls in the bag, and out of those, 4 are red. Probability is calculated by dividing the number of favorable outcomes by the total number of outcomes. Since (\frac{4}{12}) simplifies to (\frac{1}{3}), the probability of randomly selecting a red ball is (\frac{1}{3}). This means that, on average, one out of every three selections would result in a red ball if you repeated this experiment many times.