 Discrete Mathematics

# 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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