Hugo plans to buy packs of baseball cards until he gets the card of his favorite player, but he only has enough money to buy at most 4 packs. Suppose that each pack has a probability of 0.2 of containing the card Hugo is hoping for.

Let the random variable X be the number of packs of cards Hugo buys. Here is the probability distribution for X:

What is the probability that Hugo buys fewer than 3 packs of cards?

A data scientist tracked how many cups of coffee she drank every day at work over the course of a year. She used the data to build a probability distribution where the random variable C represents the number of cups of coffee she drank on a given day. Here is the partially completed distribution:

Cora is playing a game that involves flipping three coins at once.

Let the random variable H be the number of coins that land showing "heads". Here is the probability distribution for H:

Can the function in the given table be a probability distribution function?

• Yes, because all the probabilities are between 0 and 1

• No, because the sum of the probabilities is not 1

• Yes, because the sum of the probabilities is 1

• Yes, because it is in a table format.

• No, because some probabilities are less than zero.

The function in the given table is a probability distribution function of a discrete random variable 𝑋. Find the value of 𝑎.

Write your answer as a fraction in its simplest form. use the / symbol e.g. 1/3

Let 𝑋 be the random variable that represents the number of patients who visit a dental clinic per hour. The probability distribution of 𝑋 is shown in the table below.

Find the probability that exactly 13 patients visit the clinic in a given hour.

(write your answers to 2 decimal places)

Let 𝑋 be the random variable that represents the number of patients who visit a dental clinic per hour. The probability distribution of 𝑋 is shown in the table below.

Find the probability that at least 13 patients visit the clinic in a given hour.

(write your answers to 2 decimal places)

Let 𝑋 be the random variable that represents the number of patients who visit a dental clinic per hour. The probability distribution of 𝑋 is shown in the table below.

Find the probability that at most 13 patients visit the clinic in a given hour.

(write your answers to 2 decimal places)