A researcher used regression analysis to study the relationship between the number of hours students studied and their final exam scores in a statistics course. The regression output below was generated using data from $15$ students. The model was then used to predict the exam score for a student who studied for $8$ hours. What is the predicted student's exam score?

A computer program randomly generates a digit from $0$ to $9$. What is the sample space for this experiment, and how many possible outcomes are there?

A hospital has $3,200$ nurses and $1,800$ doctors. Of the nurses, $480$ have completed advanced training, while $720$ doctors have completed advanced training. Are the events "being a nurse" and "having completed advanced training" independent?

In a manufacturing process, the probability that an item is defective is $0.474$. For a quality check involving four randomly selected items, determine the following:

The probability that all four items are non-defective.

A cafe analyzed whether customers tipped based on their payment method. Some customers paid with cash, while others paid by card. The results are shown below:

What is the probability that a customer did not tip, given that the customer paid by card?

The probability that an event $E$ will not occur is given below. Find the probability that the event will occur.

$P\left(\bar{E}\right)=0.86$

A survey of $800$ college students was conducted to study risky behaviors. The results showed the following:

• $280$ students admitted to speeding regularly.
• $190$ students admitted to using their phones while biking.
• $60$ students admitted to doing both.

If one student is randomly selected from this group, what is the probability that the student either sped regularly or used a phone while biking, but not both?

If the probability of event A is 0.2 and the probability of event B is 0.3, what is the probability of either event A or event B occurring if they are mutually exclusive?

A consumer feedback agency surveyed $1115$ shoppers to assess their opinions on a new store policy that limits return periods to $7$ days. The summary of responses is shown in the Pareto chart. What is the probability of selecting a shopper who believes the policy is extremely unfair?