# Algebra 2 Probability

posted by Johnny

There are 10 cards. Each card has one number between 1 and 10, so that every number from 1 to 10 appears once.
In which distributions does the variable X have a binomial distribution?

When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen.

When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen.

When a card is chosen at random without replacement three times, X is the number of times an even number is chosen.

When a card is chosen at random with replacement multiple times, X is the number of times a card is chosen until a 5 is chosen.

1. Arora

In a binomial distribution, the probability of the event happening (and not happening) must remain constant in all trials. This occurs when the removed card is replaced, and not when the removed card remains unreplaced.

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