A die is tossed 120 times. Find the probability of getting the following results. More than fift

step 1 In this problem, we have a dye being tossed 120 times, and we're asking the probability that the

A die is tossed 120 times. Find the probability of getting...

Key Concepts

Tail Probability and Complement Rule

Tail probability involves finding the probability that a random variable takes on a value greater than a specific threshold. In many cases, this is efficiently computed using the complement rule, where one subtracts the cumulative probability up to the threshold from one. This approach is particularly useful when summing individual probabilities directly is complex or cumbersome.

Normal Approximation

Normal approximation is a method used to approximate the binomial distribution by a normal distribution when the number of trials is large enough, and the conditions np and n(1-p) are sufficiently high. This approximation simplifies the computation of tail probabilities, like the probability of exceeding a certain number of successes, by using the properties of the normal distribution.

Binomial Distribution

The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success. In the context of repeated experiments—like tossing a die—the number of times a specific outcome occurs can be modeled by the binomial distribution, provided each trial is independent and has a constant probability of yielding that outcome.

Bernoulli Trial

A Bernoulli trial is a random experiment with exactly two possible outcomes, often termed “success” and “failure”. Each die toss where one checks for a particular outcome (for instance, rolling a specific number) represents a Bernoulli trial, with the probability of success being the likelihood of the desired outcome, and the probability of failure being its complement.

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