For the 50 students in an art contest, there will be 1 prize for first place, 1 prize for second place, and 3 prizes for honorable mention. What is the probability of winning a prize? A: 0.5 B: 5 C: 1 D: 0.1
The correct answer and explanation is:
The total number of students in the contest is 50. There are 1 prize for first place, 1 prize for second place, and 3 prizes for honorable mention, so there are 5 prizes in total. To find the probability of winning a prize, we need to calculate how many favorable outcomes there are and divide by the total number of possible outcomes.
Since there are 5 prizes and 50 students, the probability of any student winning a prize is: Probability of winning a prize=Number of prizesTotal number of students=550=0.1\text{Probability of winning a prize} = \frac{\text{Number of prizes}}{\text{Total number of students}} = \frac{5}{50} = 0.1
Thus, the correct answer is D: 0.1.
In a probability context, the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the favorable outcomes are the 5 prizes, and the total possible outcomes are the 50 students. This means that each student has a 0.1 or 10% chance of winning a prize. This is a basic example of calculating probability, where the favorable events (winning a prize) are out of the total possible events (the students competing).