To explore whether the statement "Probability can never be equal to 154" is true, let us understand the basic principles of probability.
1. Definition of Probability:
Probability is a measure of the likelihood of an event to occur. It is quantified as a number between 0 and 1, where:
- 0 indicates that the event cannot occur (impossible event).
- 1 indicates that the event is certain to occur.
2. Mathematical Range of Probability:
In mathematical terms, the range of any probability value [tex]\( P(E) \)[/tex] of an event [tex]\( E \)[/tex] is:
[tex]\[
0 \leq P(E) \leq 1
\][/tex]
3. Explanation with Examples:
- If you flip a fair coin, the probability of getting heads is [tex]\( P(\text{Heads}) = \frac{1}{2} = 0.5 \)[/tex].
- The probability of rolling a 6 on a fair six-sided die is [tex]\( P(\text{Rolling a 6}) = \frac{1}{6} \approx 0.167 \)[/tex].
4. Evaluating the Given Statement:
- The statement says "Probability can never be equal to 154".
- Given the range of probabilities is strictly between 0 and 1 (inclusive), a probability of 154 is indeed impossible.
Therefore, the statement "Probability can never be equal to 154" is true.
So the correct answer is:
True
