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# Discrete Probability Distributions

What is the probability that the sum of two dice will be less than 5? How many throws will it take you to hit your first "bullseye" on a dart board? Use discrete probability distributions to find out!

# Binomial Distribution

A basketball player is practicing 3-pointers. If the probability that he successfully scores each shot is $$\frac{4}{5},$$ what is the expected value of the points he scores after throwing $$100$$ shots?

Note: The player scores 3 points for each successful shot.

A basketball player is practicing 3-pointers. If the probability that he successfully scores each shot is $$\frac{3}{5},$$ what is the variance of the points he scores after throwing $$800$$ shots?

Note: The player scores 3 points for each successful shot.

Reina throws a fair die $$16$$ times. What is the sum of the expected value and variance of the number of trials where she gets a multiple of 3?

A die is thrown $$21$$ times. Getting number $$4$$ is considered a success. The variance of the distribution of the number of successes is $$\text{_________}.$$

The probability of success in sending a character by wireless is $$p = \frac{3}{7}.$$ What is the probability that $$2$$ characters out of $$4$$ are sent successfully?

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