Probability

# 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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