Question

5-) Compute the probabilities of getting the following number of aces ν=0,1,2,3,4 in a throw of four dice. Plot them in a histogram.

Answer 1

The probabilities of getting 0, 1, 2, 3, or 4 aces in a throw of four dice can be calculated using the binomial probability distribution formula. A histogram can be plotted to visualize the probabilities associated with each number of aces.

Step-by-step explanation:

Using the binomial probability formula, the probability of obtaining a certain number of aces in a given number of trials can be calculated. In this case, the probability of getting an ace on a single die throw is 1/6.

The binomial probability formula is used to find the probability of getting a specific number of successes (aces, in this case) in a fixed number of independent trials. Each trial in this context is a die throw, and the total number of trials is four (for the four dice).

By applying the formula for different values of ν (0, 1, 2, 3, 4), you can calculate the respective probabilities. These probabilities represent the likelihood of getting 0, 1, 2, 3, or 4 aces in a throw of four dice. Once these probabilities are computed, they can be plotted in a histogram to visualize the distribution and relative likelihood of each outcome. The histogram helps in understanding the probability distribution of obtaining different numbers of aces in the given scenario.