The teacher gave a true or false quiz where [tex]P(\text{true})=0.7[/tex] for each question. Interpret the likelihood that the first question will be true.

A. Likely.
B. Unlikely.
C. Equally likely and unlikely.
D. This value is not possible to represent the probability of a chance event.



Answer :

To determine the likelihood that the first question in the quiz will be true, we start by looking at the provided probability value, [tex]\(P(\text{true}) = 0.7\)[/tex].

1. Understanding Probability Values: Probabilities range from 0 to 1:
- A probability of 0 means an event will not occur.
- A probability of 1 means an event will definitely occur.
- A probability of 0.5 means an event is equally likely to occur or not occur.

2. Interpretation of Given Probability:
- In this case, [tex]\(P(\text{true}) = 0.7\)[/tex].
- This means there is a 70% chance that the first question will be true.

3. Categorizing the Likelihood:
- A probability greater than 0.5 indicates that the event is more likely to occur than not.
- If the probability is much closer to 1 than to 0.5, it means the event is quite likely.

Given that 0.7 is significantly greater than 0.5, we interpret this probability as follows:
- It is Likely that the first question in the quiz will indeed be true.

So, the appropriate interpretation of [tex]\(P(\text{true}) = 0.7\)[/tex] is:

Likely.

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