Which of these is a probability value?
a. -0.25
b. 1/4
c. 37
d. 1.3
e. 2 5/9
The correct answer and explanation is:
The correct answer is b. 1/4.
A probability value is a numerical representation of the likelihood of an event occurring, and it must lie between 0 and 1, inclusive. That means the probability of an event can never be negative and cannot exceed 1. Here’s a breakdown of each option:
- a. -0.25: This is a negative number, which is not a valid probability. Probabilities can only range from 0 (impossible event) to 1 (certain event). Hence, this is not a valid probability value.
- b. 1/4: This is a fraction that represents a probability value. Since 1/4 equals 0.25, it lies between 0 and 1, making it a valid probability value. It means there is a 25% chance of an event occurring.
- c. 37: This is a large number greater than 1. Probabilities cannot exceed 1, so this is not a valid probability value. A probability greater than 1 doesn’t make sense in the context of likelihood.
- d. 1.3: This is a number greater than 1, which is not a valid probability value. Again, probabilities must lie between 0 and 1, so 1.3 is not valid.
- e. 2 5/9: This is an improper fraction greater than 1 (approximately 2.56), and like the others greater than 1, it is not a valid probability value.
Key Point:
Probabilities always fall within the range of 0 to 1. A probability of 0 indicates that an event will not occur, while a probability of 1 indicates that the event is certain to occur. Any number outside this range, whether negative or greater than 1, does not represent a valid probability.
Thus, the only option that satisfies the condition of a valid probability is 1/4, or 0.25.