Questions: Which of the following could be a probability? 2.9 -0.41379310344828 0.3448275862069 2.3793103448276

Solution Steps

A probability is a measure of the likelihood that an event will occur. It must satisfy the following conditions:

1. The probability of an event is a number between 0 and 1, inclusive. That is, \( 0 \leq P(A) \leq 1 \).
2. The probability of an impossible event is 0.
3. The probability of a certain event is 1.

We are given the following numbers:

1. \( 2.9 \)
2. \( -0.41379310344828 \)
3. \( 0.3448275862069 \)
4. \( 2.3793103448276 \)

We need to determine which of these numbers could be a probability.

1. \( 2.9 \):

   • This number is greater than 1, which violates the condition \( 0 \leq P(A) \leq 1 \).
   • Therefore, \( 2.9 \) cannot be a probability.

2. \( -0.41379310344828 \):

   • This number is negative, which violates the condition \( 0 \leq P(A) \leq 1 \).
   • Therefore, \( -0.41379310344828 \) cannot be a probability.

3. \( 0.3448275862069 \):

   • This number is between 0 and 1, satisfying the condition \( 0 \leq P(A) \leq 1 \).
   • Therefore, \( 0.3448275862069 \) could be a probability.

4. \( 2.3793103448276 \):

   • This number is greater than 1, which violates the condition \( 0 \leq P(A) \leq 1 \).
   • Therefore, \( 2.3793103448276 \) cannot be a probability.

Final Answer